Robust nonhyperbolic dynamics and heterodimensional cycles

DOI10.1017/S0143385700008385zbMath0831.58035OpenAlexW1967721363MaRDI QIDQ4835544

Lorenzo J. Dıaz

Publication date: 6 June 1995

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700008385

zbMATH Keywords

bifurcationparametrized families of diffeomorphisms

Mathematics Subject Classification ID

Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (19)

Connexions hétéroclines et généricité d'une infinité de puits et de sources ⋮ Determining the global manifold structure of a continuous-time heterodimensional cycle ⋮ Persistent homoclinic tangencies and the unfolding of cycles ⋮ Closing lemmas ⋮ Germ-typicality of the coexistence of infinitely many sinks ⋮ Mingled hyperbolicities: ergodic properties and bifurcation phenomena (an approach using concavity) ⋮ Homoclinic bifurcations that give rise to heterodimensional cycles near a saddle-focus equilibrium ⋮ Robust tangencies of large codimension ⋮ Multichaos from Quasiperiodicity ⋮ Growth of number of periodic orbits of one family of skew product maps ⋮ Blender-horseshoes in Center-unstable Hénon-like Families ⋮ Hénon-Like Families and Blender-Horseshoes at Nontransverse Heterodimensional Cycles ⋮ Existence of heterodimensional cycles near shilnikov loops in systems with a \(\mathbb{Z}_2\) symmetry ⋮ Degenerate bifurcations of nontwisted heterodimensional cycles with codimension 3 ⋮ A global perspective for non-conservative dynamics ⋮ Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors ⋮ Newhouse phenomenon and homoclinic classes ⋮ Partial hyperbolicity and robust transitivity ⋮ Maps close to identity and universal maps in the Newhouse domain

Cites Work

• Unnamed Item
• The dynamics of the Hénon map
• Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms
• Hyperbolicity and the creation of homoclinic orbits
• On the \(C^ 1\Omega\)-stability conjecture
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Abundance of strange attractors
• Homoclinic tangencies for hyperbolic sets of large Hausdorff dimension
• Diffeomorphisms with infinitely many sinks
• Partially hyperbolic fixed points
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Cascades of period-doubling bifurcations: A prerequisite for horseshoes
• Nonconnected heterodimensional cycles: bifurcation and stability

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