Downloads & Free Reading Options - Results

We study a class of quadratic, infinite-dimensional dynamical systems, inspired by models for viscoelastic fluids. We prove that these equations define a semi-flow on the cone of positive, essentially bounded functions. As time tends to infinity, the solutions tend to an equilibrium manifold in the $L^2$-norm. Convergence to a particular function on the equilibrium manifold is only proved under additional assumptions. We discuss several possible generalizations.

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

Invariant torus are constructed under assumption that the homogeneous system admits an exponential dichotomy on the semi-axes. The main result is closely related with the well-known Palmer's lemma and results of Boichuk A.A., Samoilenko A.M.

The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fr\'{e}chet space. The other is about the chaoticity of a translation map in the space of real continuous functions. The chaos is shown in the senses of both Li-Yorke and Wiggins. Treating dimensions as freedoms, the two results imply that in the case of an infinite number of freedoms, a system may exhibit complexity even when the action is linear. Finally, the authors discuss physical applications of infinite-dimensional linear chaotic dynamical systems.

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the canonical symplectic structure are borrowed from the Cartan's theory of differential systems on associated jet--manifolds. The symmetry structure reduced on the invariant submanifolds of critical points of some nonlocal Euler--Lagrange functional is described thoroughly for both differential and differential discrete dynamical systems. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integral-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Backlund transformation. The connection of this hierarchy with integrable by Lax spatially two-dimensional systems is studied.

We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Webster's model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave equation on 3D waveguides. The two models are treated in an unified fashion so that the results on the wave equation reduce to the corresponding results of approximating Webster's model at the limit of vanishing waveguide intersection.

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of Brownian motion. Proofs of large deviations properties are reduced to demonstrating basic qualitative properties (existence, uniqueness and tightness) of certain perturbations of the original process.

The speakers gave reports on their research to-date concerning nonlinear Partial Differential Equations and possible systems of Ordinary Differential Equations which faithfully capture their essential behavior, particularly in terms of chaotic behavior.

In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a continuous random map has a positive topological entropy, then it contains a topological horseshoe. We also show that the positive topological entropy implies the chaos in the sense of Li-Yorke. The complicated behavior exhibiting here is induced by the positive entropy but not the randomness of the system.

In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a continuous random map has a positive topological entropy, then it contains a topological horseshoe. We also show that the positive topological entropy implies the chaos in the sense of Li-Yorke. The complicated behavior exhibiting here is induced by the positive entropy but not the randomness of the system.

The main goal of the research is to understand nonlinear processes in natural phenomena. There is a strong emphasis on nonlinear optics, a subject which is relatively young and extremely rich in scientific and technological potential. Turbulence in optics, the study of the complex space-time patterns and defects which appear in feedback cavities and counterpropagating beams, is more analytically tractable than its counterpart in fluids, and is currently international attention. It is the subject of our latest workshop. The primary goal of the Center is to provide an environment for research and learning in the Mathematical Sciences. Its basic research themes are the modelling, understanding and applicability of nonlinear processes in optics, fluids, neural networks, and random distributed systems with continuing investigations into pattern dynamics, percolation, behavior of lattice gases, nonlinear stability, low dimensional chaos, turbulence, dynamical systems and the nature of integrable systems of differential equations.

This was a conference grant for the conference 'Geometric Methods for Infinite-Dimensional Dynamical Systems' held November 4-6, 2011 at Brown University. The plenary and topical talks formed the heart of the conference. They featured the four mathematical themes of the conference: data assimilation, geometric singular perturbation theory, nonlinear optics and traveling waves.

We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does not exist (or not known to exist).

This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable manifolds of a finite number of hyperbolic equilibrium solutions, we prove that the perturbed non-autonomous system has exactly the same number of almost periodic solutions. As a consequence, the pullback attractor of the perturbed system is given by the union of unstable manifolds of these finitely many almost periodic solutions. An application of the result to the Chafee-Infante equation is discussed.

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of Brownian motion. Proofs of large deviations properties are reduced to demonstrating basic qualitative properties existence, uniqueness, and tightness of certain perturbations of the original process.

An approach is outlined for the discussion of the qualitative theory of infinite dimensional dynamical systems. Retarded functional differential equations are used to illustrate the usefulness of the approach and the limitations of our present knowledge. (Author)

A subject of investigation was the extent to which an entropy inequality (i.e., the Second Law of Thermodynamics) induces stabilization of solutions of hyperbolic systems of conservation laws. It was shown that the entropy inequality guarantees uniqueness of Lipschitz solutions within the class of BV solutions, provided that the entropy is convex just in certain directions compatible with the natural invariance of the system expressed in terms of involutions . It was proven that BV solutions of strictly hyperbolic systems with shocks of moderate strength, which satisfy the Liu admissibility condition, minimize the rate of total entropy production. The theory of generalized characteristics for a single conservation law, developed earlier by the author, was applied to conservation laws with inhomogeneity and fading memory. The theory of generalized characteristics was developed for systems of conservations laws and was used to obtain information on the large time behavior of solutions. This theory was employed to establish uniqueness of solutions for special systems of conservation laws in which shock and rarefaction wave curves coincide.

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

This was the weekly poetry project for 3 June 2006. Many “character” poems cut straight to the inmost psychology of their subjects, but here, the eponymous Richard Cory with all his wealth and charm is viewed entirely from the outside. Indeed as the poem ends, we realise with an unforgettable shock just how little we, the narrator, or perhaps anyone really knew about him. (Summary by LauraFox)

LibriVox volunteers bring you 16 different recordings of <em>The House on the Hill</em> by Edwin Arlington Robinson. This was the weekly poetry project for the week of September 30th, 2007.

3Longhead: The Story of the First Fire

By C. H. Robinson

A fictionalized version of the self-discovery of primitive man, including: fire, cooking, defense and protection, architecture, community, communication, religion, government, and social interaction - Summary by Nick Bulka

4Man Against the Sky: A Book of Poems

By Edwin Arlington Robinson

This is a volume of later Poetry by the famous American poet Edwin Arlington Robinson. - Summary by Carolin

5Three Taverns: A Book of Poems

By Edwin Arlington Robinson

This is a volume of poems by Edwin Arlington Robinson. This volume contains, among other poems, the famous poems The Valley of the Shadow and Lazarus. - Summary by Carolin

6Children of the Night

By Edwin Arlington Robinson

This is a collection of poems by Edwin Arlington Robinson, titled the Children of the Night, and including, besides the famous title poem, several ballads, and poems dedicated to other authors and poets. - Summary by Carolin

This is a volume of narrative poems by Edwin Arlington Robinson. - Summary by Carolin

This is a volume of poetry by Edwin Arlington Robinson, dedicated to Theodore Roosevelt. This volume also contains his lesser known shorter poems as well as the well-known narrative poem <i>Miniver Cheevy</i>. - Summary by Carolin

Margaret of Angoulême, Queen of Navarre (Marguerite de Navarre), (1492-1549), was the sister of Francis I, King of France. She was highly-educated and was courted by the future Henry VIII of England. However, at the age of seventeen, she was married by royal decree to the untutored dolt, Charles IV of Alençon. After his death she wed Henry II of Navarre by whom she had a daughter (the mother of the future Henry IV of France) and a son, who died in infancy. The author takes us with Margaret on her perilous journey over the Pyrenees to Spain to attempt to free her brother, Francis, held captive by the Holy Roman Emperor. Margaret's support for the first stirrings of the Reformation in France alarmed the Catholic conservatives of the Sorbonne. Her cycle of short stories, the "Heptameron," is still read and enjoyed today. (Pamela Nagami)

Emily Brontë (1818-1848) is best known for her only novel, "Wuthering Heights." She was born in Yorkshire, northern England, where her father was an Anglican curate. When Brontë was three years old her mother died of cancer. At the age of six she joined her three sisters briefly at the Clergy Daughters' School, where privations and abuse contributed to the deaths of two of them. Her elder sister, Charlotte, immortalized this terrible place in "Jane Eyre." In 1846 Emily Brontë, under the pseudonym Ellis Bell, published a selection of her poetry. In 1847 appeared her dark, gothic novel, "Wuthering Heights," with its Byronic anti-hero, Heathcliff. Brontë was shy, even reclusive, and never married. In the fall of 1848 she fell ill with inflammation of the lungs, probably due to rapidly-progressive tuberculosis, and died in December of that year, aged twenty-nine. This is a short biography of Brontë written by the British poet, novelist, and critic, Agnes Mary Frances Robinson (1857-1944). (Pamela Nagami)

11Life Story of a Black Bear

By Harry Perry Robinson

This is the life story of a Black Bear in the western US, as told by the bear himself. He tells of the days when humans began to invade the territory where they and their ancestors had been kings for many eons. - Summary by philip chenevert

12In New England Fields and Woods

By Rowland E. Robinson

Born in rural Vermont in 1833, and nearly unknown to today's readers, Rowland Evans Robinson was once one of Vermont's best-known writers. A talented artist, he drew cartoons in New York City for the “funny papers" before returning to Vermont, where he authored nearly a dozen widely-read books on nature and rural farm life. Poor vision progressed to blindness between the ages of 44 and 60, yet he continued to write with the aid of his wife, Anna. This collection of short essays follows New England's changing seasons and moods in all its natural beauty. - Summary by Nemo

After the Roman conquest, the Celtic Gauls adopted Roman culture and speech. The Germanic invasions ultimately transformed France into a Catholic feudal society. In this short history, Mary Duclaux traces the emergence of towns, the rise of the French monarchy, the calamitous Hundred Years' War and the Wars of Religion. We meet Joan of Arc, Charles VII, the gallant Henry IV, and the Sun King, Louis XIV, who drove France to the brink of bankruptcy. In the second half of the book Duclaux gives us the French Revolution and the Age of Napoleon: Louis XVI, sunk in "plump and smiling apathy," Marie Antoinette, who pleaded with France's enemies for rescue, the Paris mob who hated her, Danton, Saint-Just, Robespierre, and the Terror, and finally a sombre young Corsican officer with no small talk, the military and administrative genius, Napoleon Bonaparte. (Summary by Pamela Nagami, M.D.)

LibriVox readers bring you 16 recordings of "Miniver Cheevy" by Edwin Arlington Robinson. This was the fortnightly poem for June 13, 2021.<br>------ <br> "Miniver Cheevy" is a narrative poem written by Edwin Arlington Robinson and first published in The Town Down the River in 1910. The poem relates the story of a hopeless romantic who spends his days thinking about what might have been if only he had been born earlier in time. - Summary by Wikipedia

Harriet Robinson was a frequent contributor to the famous monthly periodical, "The Lowell Offering", which featured poetry, essays and fiction written between 1840-1845 by the young female textile workers (ages 15-35) known as Lowell Mill Girls, living in the innovative Lowell, Massachusetts textile mills communities. Articles published therein describe their living conditions, where they came from, how they felt about their jobs, challenges met, bosses, new experiences and education they received. Rev. A.C. Thomas who organized and edited the publication, found in these factory girls a good field for the application of his belief that women have the right and the ability to express their thoughts, both in speaking and in writing. In his own words, "...and thus was published ... the first magazine or journal written exclusively by women in all the world." Harriet continued writing for the rest of her life, including this book, largely in support of women's education, independence and suffrage. (Summary by ~ Michele Fry)

16Children of the Night

By Edwin Arlington Robinson

LibriVox volunteers bring you 16 recordings of The Children of the Night by Edwin Arlington Robinson. This was the Fortnightly Poetry project for August 14, 2022.<br> -----<br> <i>The Children of the Night</i> is from the book of the same title, by Edwin Arlington Robinson (1869-1935). He was apparently a favorite poet of Theodore Roosevelt. - Summary by Owlivia

17Bundle of Letters from over the Sea

By Louise B. Robinson

In presenting my little book to the public, I feel that I should apologize for so doing, instead of introducing it; for at the time my letters were written I had no idea of publishing them. Since my return, however, several friends who had read them have assured me that they greatly enjoyed them, and felt that others would do so, also, had they the opportunity. The letters have, at least, the merit of being fresh and honest impressions of the places described, as they were written on the spots. Remembering how eagerly I have always read letters of travel, I sincerely hope{x} that mine may prove a source of pleasure to some—to those who have been over the same ground, and to many who have the pleasure in anticipation. I am aware that the route I describe is a well-worn thoroughfare, but every eye has its own perspective, and different views of the same pictures assist the sight-seer in comprehending the whole. Therefore, I here beg the charity of all into whose hands this little book may fall. L. B. R. Hotel Oxford, Boston, December 20, 1889. - Summary by From the Preface

This volume was written by the author to help people with proper etiquette for certain social dilemma issues. i.e. male manners while being social with the opposite sex. - Summary by April