STABLE SETS OF CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE THE EXPECTED DIMENSION

DOI10.1017/S1474748019000185zbMath1462.37037arXiv1712.06629OpenAlexW2963144613MaRDI QIDQ5147678

Jean-Christophe Yoccoz, Carlos Matheus, Jacob Palis

Publication date: 27 January 2021

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.06629

zbMATH Keywords

Hausdorff dimensionheteroclinic bifurcationsnonuniformly hyperbolic horseshoes

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Dynamical systems with hyperbolic orbits and sets (37D05) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Dimension theory of smooth dynamical systems (37C45)

Cites Work

• Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles
• An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes
• Non-uniformly hyperbolic horseshoes in the standard family
• A genericC¹map has no absolutely continuous invariant probability measure

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