STABLE SETS of CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE the EXPECTED DIMENSION

Carlos Matheus; Jacob Palis; Jean Christophe Yoccoz

doi:10.1017/S1474748019000185

STABLE SETS of CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE the EXPECTED DIMENSION

Carlos Matheus
, Jacob Palis
, Jean Christophe Yoccoz

University Paris 13
IMPA
Collège de France

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We show that the stable and unstable sets of non-uniformly hyperbolic horseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms have the value conjectured in a previous work by the second and third authors of the present paper. Our results apply to first heteroclinic bifurcations associated with horseshoes with Hausdorff dimension <![CDATA[{ of conservative surface diffeomorphisms.

langue originale	Anglais
Pages (de - à)	305-329
Nombre de pages	25
journal	Journal of the Institute of Mathematics of Jussieu
Volume	20
Numéro de publication	1
Les DOIs	https://doi.org/10.1017/S1474748019000185
état	Publié - 1 janv. 2021
Modification externe	Oui

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10.1017/S1474748019000185

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title = "STABLE SETS of CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE the EXPECTED DIMENSION",

abstract = "We show that the stable and unstable sets of non-uniformly hyperbolic horseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms have the value conjectured in a previous work by the second and third authors of the present paper. Our results apply to first heteroclinic bifurcations associated with horseshoes with Hausdorff dimension \{ of conservative surface diffeomorphisms.</p>",

keywords = "Hausdorff dimension, heteroclinic bifurcations, non-uniformly hyperbolic horseshoes",

author = "Carlos Matheus and Jacob Palis and Yoccoz, \{Jean Christophe\}",

year = "2021",

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doi = "10.1017/S1474748019000185",

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T1 - STABLE SETS of CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE the EXPECTED DIMENSION

AU - Matheus, Carlos

AU - Palis, Jacob

AU - Yoccoz, Jean Christophe

PY - 2021/1/1

Y1 - 2021/1/1

N2 - We show that the stable and unstable sets of non-uniformly hyperbolic horseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms have the value conjectured in a previous work by the second and third authors of the present paper. Our results apply to first heteroclinic bifurcations associated with horseshoes with Hausdorff dimension { of conservative surface diffeomorphisms.</p>

AB - We show that the stable and unstable sets of non-uniformly hyperbolic horseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms have the value conjectured in a previous work by the second and third authors of the present paper. Our results apply to first heteroclinic bifurcations associated with horseshoes with Hausdorff dimension { of conservative surface diffeomorphisms.</p>

KW - Hausdorff dimension

KW - heteroclinic bifurcations

KW - non-uniformly hyperbolic horseshoes

U2 - 10.1017/S1474748019000185

DO - 10.1017/S1474748019000185

M3 - Article

AN - SCOPUS:85063952054

SN - 1474-7480

VL - 20

SP - 305

EP - 329

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 1

ER -

STABLE SETS of CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE the EXPECTED DIMENSION

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