✦ LIBER ✦

Chaos for some infinite-dimensional dynamical systems

✍ Scribed by Ryszard Rudnicki

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 145 KB
Volume: 27
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.498

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper is devoted to the problem of chaotic behaviour of infinite‐dimensional dynamical systems. We give a survey of different approaches to study of chaotic behaviour of dynamical systems. We mainly discuss the ergodic‐theoretical approach to chaos which bases on the existence of invariant measures having strong analytic and mixing properties. This method is applied to study chaotic behaviour of semiflows generated by semilinear partial differential equations and linear transformations. Copyright © 2004 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

Lyapunov Functions for Infinite-Dimensio

Lyapunov Functions for Infinite-Dimensional Systems

✍ Maciej Kocan; Pierpaolo Soravia 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 203 KB

We study Lyapunov functions for infinite-dimensional dynamical systems governed by general maximal monotone operators. We obtain a characterization of Lyapunov pairs by means of the associated Hamilton-Jacobi partial differential equations, whose solutions are meant in the viscosity sense, as evolve

Generalized Invariant Subspaces for Infi

Generalized Invariant Subspaces for Infinite-Dimensional Systems

✍ Naohisa Otsuka; Haruo Hinata 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 125 KB

In this paper some generalized invariant subspaces for infinite-dimensional systems are investigated, and then some sufficient conditions for parameter-insensitive disturbance-rejection problems with state feedback and with measurement output feedback to be solvable are studied.

Approximation of Transfer Functions of I

Approximation of Transfer Functions of Infinite Dimensional Dynamical Systems by Rational Interpolants with Prescribed Poles

✍ Angel Ribalta Stanford; Guillermo López Lagomasino 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 171 KB

Rational interpolants with prescribed poles are used to approximate holomorphic functions on the closure of their region of analyticity under natural assumptions of their properties on the boundary. The transfer functions of some infinite dimensional dynamical systems of interest in applications sat

Dimensionality reduction for uncertain d

Dimensionality reduction for uncertain dynamic systems

✍ Sean Kenny; Luis Crespo; Dan Giesy 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 269 KB

On Differential Games for Infinite-Dimen

On Differential Games for Infinite-Dimensional Systems with Nonlinear, Unbounded Operators

✍ Maciej Kocan; Pierpaolo Soravia; Andrzej Swiech 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 319 KB

We consider a two-player, zero-sum differential game governed by an abstract nonlinear differential equation of accretive type in an infinite-dimensional space. We prove that the value function of the game is the unique viscosity solution of the corresponding Hamilton᎐Jacobi᎐Isaacs equation in the s

H∞ control and filtering with initial un

H∞ control and filtering with initial uncertainty for infinite dimensional systems

✍ Akira Ichikawa 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 909 KB

The H,-control problem with a non-zero initial condition for infinite dimensional systems is considered The initial conditions are assumed to be in some subspace. First the H , problem with full information is considered and necessary and sufficient conditions for the norm of an input-output operato