Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations

Dmitry Turaev; Sergey Zelik

doi:10.1088/0951-7715/16/6/317

Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations

Dmitry Turaev, Sergey Zelik

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A new method of obtaining lower bounds for the attractor's dimension is suggested which involves analysis of homoclinic bifurcations. The method is applied for obtaining sharp estimates of the attractor's dimension for a class of abstract damped wave equations which are beyond the reach of the classical methods.

Original language	English
Pages (from-to)	2163-2198
Number of pages	36
Journal	Nonlinearity
Volume	16
Issue number	6
DOIs	https://doi.org/10.1088/0951-7715/16/6/317
State	Published - 1 Nov 2003
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy (all)
Applied Mathematics

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10.1088/0951-7715/16/6/317

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title = "Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations",

abstract = "A new method of obtaining lower bounds for the attractor's dimension is suggested which involves analysis of homoclinic bifurcations. The method is applied for obtaining sharp estimates of the attractor's dimension for a class of abstract damped wave equations which are beyond the reach of the classical methods.",

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AU - Zelik, Sergey

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Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations

Abstract

ASJC Scopus subject areas

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