Homoclinic tangencies for hyperbolic sets of large Hausdorff dimension

DOI10.1007/BF02392792zbMath0801.58035MaRDI QIDQ1327357

Jean-Christophe Yoccoz, Jacob Palis

Publication date: 4 December 1994

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensionsymbolic dynamicshyperbolicity

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Low-dimensional dynamical systems (37E99) Dynamical systems with hyperbolic behavior (37D99)

Related Items (18)

Non-periodic bifurcations for surface diffeomorphisms ⋮ On the measure of arithmetic sums of Cantor sets ⋮ Persistent homoclinic tangencies and the unfolding of cycles ⋮ How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency ⋮ On the arithmetic sum of regular Cantor sets ⋮ Robust nonhyperbolic dynamics and heterodimensional cycles ⋮ Persistence of homoclinic tangencies in higher dimensions ⋮ Prevalent dynamics at the first bifurcation of Hénon-like families ⋮ Splitting and coexistence of 2-D strange attractors in a general family of Expanding Baker Maps ⋮ Strictly invariant sets for 2-D tent maps: 2-D strange attractors ⋮ Expanding Baker maps as models for the dynamics emerging from 3D homoclinic bifurcations ⋮ Intersecting self-similar Cantor sets ⋮ Topological structure of (partially) hyperbolic sets with positive volume ⋮ Abundance of hyperbolicity in the $C^1$ topology ⋮ Renormalizable expanding Baker maps: coexistence of strange attractors ⋮ A global perspective for non-conservative dynamics ⋮ Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles ⋮ A Frostman-Type Lemma for Sets with Large Intersections, and an Application to Diophantine Approximation

Cites Work

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• The dynamics of the Hénon map
• Bifurcation to infinitely many sinks
• Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms
• Hyperbolicity and the creation of homoclinic orbits
• Hausdorff dimension of quasi-circles
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Abundance of strange attractors
• The Hausdorff dimension of horseshoes of diffeomorphisms of surfaces
• Hausdorff dimension for horseshoes
• Cascades of period-doubling bifurcations: A prerequisite for horseshoes
• Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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