How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency

DOI10.1016/j.aim.2006.03.012zbMath1110.37034OpenAlexW1983783500MaRDI QIDQ861055

Vadim Yu. Kaloshin, A. S. Gorodetskii

Publication date: 9 January 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2006.03.012

zbMATH Keywords

prevalencehomoclinic tangencynon-uniform hyperbolicityinfinitely many coexisting sinksnewhouse domain

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

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Cites Work

• The dynamics of the Hénon map
• Bifurcation to infinitely many sinks
• A two-dimensional mapping with a strange attractor
• How often do simple dynamical processes have infinitely many coexisting sinks?
• Hyperbolicity and the creation of homoclinic orbits
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Wild hyperbolic sets, yet no chance for the coexistence of infinitely many KLUS-simple Newhouse attracting sets
• Existence of generic homoclinic tangencies for Hénon mappings
• Infinitely many coexisting strange attractors
• Topology of generic multijet preimages and blow-up via Newton interpolation
• On models with non-rough Poincaré homoclinic curves
• Abundance of strange attractors
• Homoclinic tangencies for hyperbolic sets of large Hausdorff dimension
• Infinitely many periodic attractors for holomorphic maps of 2 variables
• Attractors and time averages for random maps
• Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
• Diffeomorphisms with infinitely many sinks
• On sets of Haar measure zero in abelian Polish groups
• Unfolding homoclinic tangencies inside horseshoes: hyperbolicity, fractal dimensions and persistent tangencies
• A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I
• A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II
• Fers à cheval non uniformément hyperboliques engendrés par une bifurcation homocline et densité nulle des attracteurs
• A quantitative version of the Kupka-Smale theorem
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• COMPLEXITY OF HOMOCLINIC BIFURCATIONS AND Ω-MODULI
• Prevalence. An addendum to: “Prevalence: a translation-invariant ‘almost every’ on infinite-dimensional spaces” [Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 2, 217–238; MR1161274 (93k:28018)]
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II
• Prevalence
• Strange attractors with one direction of instability
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