SURVEY Towards a global view of dynamical systems, for the C1-topology
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Publication:3018650
DOI10.1017/S0143385710000891zbMath1256.37006MaRDI QIDQ3018650
Publication date: 27 July 2011
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Generic properties, structural stability of dynamical systems (37C20) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)
Related Items (23)
Robust criterion for the existence of nonhyperbolic ergodic measures ⋮ Hyperbolicity versus weak periodic orbits inside homoclinic classes ⋮ Specification and partial hyperbolicity for flows ⋮ Tame dynamics and robust transitivity chain-recurrence classes versus homoclinic classes ⋮ Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles ⋮ Flexible periodic points ⋮ Homoclinic tangencies leading to robust heterodimensional cycles ⋮ Germ-typicality of the coexistence of infinitely many sinks ⋮ Dominated Pesin theory: convex sum of hyperbolic measures ⋮ Heterogeneity of the attractor of the Lorenz '96 model: Lyapunov analysis, unstable periodic orbits, and shadowing properties ⋮ Constructing center-stable tori ⋮ Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms ⋮ Volume hyperbolicity and wildness ⋮ Wild Milnor attractors accumulated by lower-dimensional dynamics ⋮ Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication ⋮ Partial hyperbolicity and homoclinic tangencies ⋮ Partial hyperbolicity and specification ⋮ Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes ⋮ Periodic measures and partially hyperbolic homoclinic classes ⋮ Fragile cycles ⋮ Maps close to identity and universal maps in the Newhouse domain ⋮ Density of hyperbolicity for classes of real transcendental entire functions and circle maps ⋮ Nontransverse heterodimensional cycles: Stabilisation and robust tangencies
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