Homoclinic tangencies and dominated splittings

DOI10.1088/0951-7715/15/5/306zbMath1011.37011OpenAlexW2003707132MaRDI QIDQ4780471

Lan Wen

Publication date: 9 June 2003

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/15/5/306

zbMATH Keywords

diffeomorphismsstable and unstable manifoldshyperbolic periodic orbithigher-dimensional casespreperiodic sets

Mathematics Subject Classification ID

Generic properties, structural stability of dynamical systems (37C20) Dynamical systems with hyperbolic orbits and sets (37D05) Partially hyperbolic systems and dominated splittings (37D30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (37)

On the abundance of Sinai-Ruelle-Bowen measures ⋮ Conditions for dominated splittings ⋮ \(C^1\)-stably shadowable chain components are hyperbolic ⋮ Hyperbolicity versus weak periodic orbits inside homoclinic classes ⋮ Tame dynamics and robust transitivity chain-recurrence classes versus homoclinic classes ⋮ A $C^2$ generic trichotomy for diffeomorphisms: Hyperbolicity or zero Lyapunov exponents or the $C^1$ creation of homoclinic bifurcations ⋮ Flexible periodic points ⋮ Closing lemmas ⋮ A countable partition for singular flows, and its application on the entropy theory ⋮ \(C^1\) weak Palis conjecture for nonsingular flows ⋮ Partial hyperbolicity far from homoclinic bifurcations ⋮ Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov ⋮ Chain components with \(C^1\)-stably orbital shadowing ⋮ C¹-stably shadowable chain components ⋮ On the partial hyperbolicity of robustly transitive sets with singularities ⋮ NON-HYPERBOLIC ERGODIC MEASURES AND HORSESHOES IN PARTIALLY HYPERBOLIC HOMOCLINIC CLASSES ⋮ Symbolic extensions and dominated splittings for generic \(C^1\)-diffeomorphisms ⋮ Local perturbations of conservativeC¹diffeomorphisms ⋮ A sufficient condition for zero entropy ⋮ Dense heteroclinic tangencies near a Bykov cycle ⋮ Equivalent conditions of dominated splitting for volume-preserving diffeomorphisms ⋮ Dominated splitting versus small angles ⋮ SURVEY Towards a global view of dynamical systems, for the C¹-topology ⋮ On the existence of attractors ⋮ An extension of the ergodic closing lemma ⋮ On the finiteness of uniform sinks ⋮ Codimension one generic homoclinic classes with interior ⋮ A global perspective for non-conservative dynamics ⋮ On the existence of non-trivial homoclinic classes ⋮ On Araujo's theorem for flows ⋮ Density of hyperbolicity and tangencies in sectional dissipative regions ⋮ A Franks’ lemma that preserves invariant manifolds ⋮ Newhouse phenomenon and homoclinic classes ⋮ Abundance of $C^{1}$-robust homoclinic tangencies ⋮ A robustly chain transitive attractor with singularities of different indices ⋮ Morse-Smale systems and horseshoes for three dimensional singular flows ⋮ Statistical properties of physical-like measures*

This page was built for publication: Homoclinic tangencies and dominated splittings