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

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

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 <![CDATA[{ of conservative surface diffeomorphisms.

Original language	English
Pages (from-to)	305-329
Number of pages	25
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	20
Issue number	1
DOIs	https://doi.org/10.1017/S1474748019000185
Publication status	Published - 1 Jan 2021
Externally published	Yes

Keywords

Hausdorff dimension
heteroclinic bifurcations
non-uniformly hyperbolic horseshoes

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10.1017/S1474748019000185

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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>",

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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

Abstract

Keywords

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