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Invariant measures for interval maps without Lyapunov exponents

Part of: Dynamical systems with hyperbolic behavior Low-dimensional dynamical systems Ergodic theory

Published online by Cambridge University Press:  15 November 2021

JORGE OLIVARES-VINALES Open the ORCID record for JORGE OLIVARES-VINALES [Opens in a new window]
JORGE OLIVARES-VINALES*
Affiliation:
Department of Mathematics, University of Rochester, Hylan Building, Rochester, NY 14627, USA Departamento de Ingeniería Matemática, Universidad de Chile, Beauchef 851, Santiago, Chile
*
e-mail: [email protected]
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Abstract

We construct an invariant measure for a piecewise analytic interval map whose Lyapunov exponent is not defined. Moreover, for a set of full measure, the pointwise Lyapunov exponent is not defined. This map has a Lorenz-like singularity and non-flat critical points.

Keywords

interval mapLyapunov exponentsergodic measures

MSC classification

Primary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
Secondary: 37A99: None of the above, but in this section
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 2 , February 2023 , pp. 663 - 691
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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