Densely branching trees as models for Hénon-like and Lozi-like attractors

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402KZH" target="_blank" >RIV/61988987:17610/23:A2402KZH - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/abs/pii/S0001870823003341?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0001870823003341?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aim.2023.109191" target="_blank" >10.1016/j.aim.2023.109191</a>

Result language

angličtina

Original language name

Densely branching trees as models for Hénon-like and Lozi-like attractors

Original language description

Inspired by a recent work of Crovisier and Pujals on mildly dissipative diffeomorphisms of the plane, we show that Hénon-like and Lozi-like maps on their strange attractors are conjugate to natural extensions (a.k.a. shift homeomorphisms on inverse limits) of maps on metric trees with dense set of branch points. In consequence, these trees very well approximate the topology of the attractors, and the maps on them give good models of the dynamics. To the best of our knowledge, these are the first examples of canonical two-parameter families of attractors in the plane for which one is guaranteed such a 1-dimensional locally connected model tying together topology and dynamics of these attractors. For the Hénon maps this applies to a positive Lebesgue measure parameter set generalizing the Benedicks-Carleson parameters, the Wang-Young parameter set, and sheds more light onto the result of Barge from 1987, who showed that there exist parameter values for which Hénon maps on their attractors are not natural extensions of any maps on branched 1-manifolds. For the Lozi maps the result applies to an open set of parameters given by Misiurewicz in 1980. Our result can be seen as a generalization to the non-uniformly hyperbolic world of a classical result of Williams from 1967. We also show that no simpler 1-dimensional models exist.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

ADV MATH

ISSN

0001-8708

e-ISSN

—

Volume of the periodical

—

Issue of the periodical within the volume

429

Country of publishing house

US - UNITED STATES

Number of pages

27

Pages from-to

1-27

UT code for WoS article

001043878300001

EID of the result in the Scopus database

2-s2.0-85164424570