Perturbation of the Lyapunov spectra of periodic orbits

J. Bochi; C. Bonatti

doi:10.1112/plms/pdr048

Perturbation of the Lyapunov spectra of periodic orbits

J. Bochi, C. Bonatti

Mathematics

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

21 Scopus citations

Abstract

We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.

Original language	English (US)
Pages (from-to)	1-48
Number of pages	48
Journal	Proceedings of the London Mathematical Society
Volume	105
Issue number	1
DOIs	https://doi.org/10.1112/plms/pdr048
State	Published - Jul 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/plms/pdr048

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abstract = "We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.",

author = "J. Bochi and C. Bonatti",

note = "Funding Information: During the preparation of this paper, the first author was partially supported by CNPq-Brazil, Faperj and Universit{\'e}de Bourgogne, and the second author was partially supported by IMPA and MathAmSud.",

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N2 - We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.

AB - We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.

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Perturbation of the Lyapunov spectra of periodic orbits

Abstract

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