Generic family with robustly infinitely many sinks

DOI10.1007/s00222-015-0632-6zbMath1365.37024arXiv1411.6441OpenAlexW1706057487MaRDI QIDQ2630283

Pierre Berger

Publication date: 26 July 2016

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.6441

zbMATH Keywords

diffeomorphismrobustnessdynamical systembasinBaire generic setPugh-Shub conjecture

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Generic properties, structural stability of dynamical systems (37C20) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (21)

On emergence and complexity of ergodic decompositions ⋮ Emergence via non-existence of averages ⋮ Almost blenders and parablenders ⋮ \(C^r\)-prevalence of stable ergodicity for a class of partially hyperbolic systems ⋮ Homoclinic tangencies leading to robust heterodimensional cycles ⋮ Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies ⋮ Emergence and non-typicality of the finiteness of the attractors in many topologies ⋮ Abundance of fast growth of the number of periodic points in two-dimensional area-preserving dynamics ⋮ Typical coexistence of infinitely many strange attractors ⋮ Complexities of differentiable dynamical systems ⋮ Steady Euler flows on \({\mathbb{R}}^3\) with wild and universal dynamics ⋮ Robust tangencies of large codimension ⋮ Dynamical systems. Abstracts from the workshop held July 11--17, 2021 (hybrid meeting) ⋮ Iterated Functions Systems, Blenders, and Parablenders ⋮ Robust degenerate unfoldings of cycles and tangencies ⋮ Attractors and skew products ⋮ Newhouse phenomenon for automorphisms of low degree in \(\mathbb{C}^3\) ⋮ Lattès maps and the interior of the bifurcation locus ⋮ Correction to: ``Generic family with robustly infinitely many sinks ⋮ Maps close to identity and universal maps in the Newhouse domain ⋮ Emergence of wandering stable components

Cites Work

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• Persistence of laminations
• The dynamics of the Hénon map
• How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency
• Quadratic maps without asymptotic measure
• Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles
• How often do simple dynamical processes have infinitely many coexisting sinks?
• Singular measures without restrictive intervals
• Sinai-Bowen-Ruelle measures for certain Hénon maps
• High dimension diffeomorphisms displaying infinitely many periodic attractors
• Regular or stochastic dynamics in real analytic families of unimodal maps
• Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
• Almost every real quadratic map is either regular or stochastic.
• Persistent nonhyperbolic transitive diffeomorphisms
• Diffeomorphisms with infinitely many sinks
• Properties of the maximal entropy measure and geometry of Hénon attractors
• Stability and bifurcations for dissipative polynomial automorphisms of \(\mathbb C^2\)
• On the inverse limit stability of endomorphisms
• Density of hyperbolicity in dimension one
• A global perspective for non-conservative dynamics
• On stability and hyperbolicity for polynomial automorphisms of C^2
• Heterodimensional tangencies
• Connexions hétéroclines et généricité d'une infinité de puits et de sources
• Hyperbolic sets exhibiting $C^1$-persistent homoclinic tangency for higher dimensions
• Open questions leading to a global perspective in dynamics
• Solution of the basin problem for Hénon-like attractors
• Stable intersections of regular Cantor sets with large Hausdorff dimensions
• On the Hausdorff dimension of Newhouse phenomena

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