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Kneading sequences for toy models of Hénon maps

Part of: Topological dynamics Low-dimensional dynamical systems

Published online by Cambridge University Press:  13 November 2020

ERMERSON ARAUJO Open the ORCID record for ERMERSON ARAUJO [Opens in a new window]
ERMERSON ARAUJO*
Affiliation:
Departamento de Matemática, Universidade Federal do Ceará, Centro de Ciências, Campus do Pici, Fortaleza – CE, CEP 60440-900, Brasil
*
e-mail: [email protected]
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Abstract

The purpose of this article is to study the relation between combinatorial equivalence and topological conjugacy, specifically how a certain type of combinatorial equivalence implies topological conjugacy. We introduce the concept of kneading sequences for a setting that is more general than one-dimensional dynamics: for the two-dimensional toy model family of Hénon maps introduced by Benedicks and Carleson, we define kneading sequences for their critical lines, and prove that these sequences are a complete invariant for a natural conjugacy class among the toy model family. We also establish a version of Singer’s theorem for the toy model family.

Keywords

combinatorial equivalencekneading sequencesunimodal maps

MSC classification

Primary: 37B10: Symbolic dynamics
Secondary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 12 , December 2021 , pp. 3521 - 3540
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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