Perturbations of attractors of differential equations

Victor A. Pliss; George R. Sell

doi:10.1016/0022-0396(91)90066-I

Perturbations of attractors of differential equations

Victor A. Pliss
, George R. Sell

School of Mathematics

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

30 Scopus citations

Abstract

In this paper we study small C¹-perturbations of a differential equation that has a hyperbolic attractor K. We show that if K has a suitable Lipschitz property and if the perturbation is small enough, then there is a homeomorphism H : K→K^Y, where K^Y is a hyperbolic attractor for the perturbed equation. Examples are included.

Original language	English (US)
Pages (from-to)	100-124
Number of pages	25
Journal	Journal of Differential Equations
Volume	92
Issue number	1
DOIs	https://doi.org/10.1016/0022-0396(91)90066-I
State	Published - Jul 1991

Bibliographical note

Funding Information:
* This research was done at the Institute for Mathematics and Its Applications supported in part by grants from the National Science Foundation.

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10.1016/0022-0396(91)90066-I

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title = "Perturbations of attractors of differential equations",

abstract = "In this paper we study small C1-perturbations of a differential equation that has a hyperbolic attractor K. We show that if K has a suitable Lipschitz property and if the perturbation is small enough, then there is a homeomorphism H : K→KY, where KY is a hyperbolic attractor for the perturbed equation. Examples are included.",

author = "Pliss, \{Victor A.\} and Sell, \{George R.\}",

note = "Funding Information: * This research was done at the Institute for Mathematics and Its Applications supported in part by grants from the National Science Foundation.",

year = "1991",

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AU - Sell, George R.

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Y1 - 1991/7

N2 - In this paper we study small C1-perturbations of a differential equation that has a hyperbolic attractor K. We show that if K has a suitable Lipschitz property and if the perturbation is small enough, then there is a homeomorphism H : K→KY, where KY is a hyperbolic attractor for the perturbed equation. Examples are included.

AB - In this paper we study small C1-perturbations of a differential equation that has a hyperbolic attractor K. We show that if K has a suitable Lipschitz property and if the perturbation is small enough, then there is a homeomorphism H : K→KY, where KY is a hyperbolic attractor for the perturbed equation. Examples are included.

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U2 - 10.1016/0022-0396(91)90066-I

DO - 10.1016/0022-0396(91)90066-I

M3 - Article

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VL - 92

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EP - 124

JO - Journal of Differential Equations

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IS - 1

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Perturbations of attractors of differential equations

Abstract

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