Wild hyperbolic sets, yet no chance for the coexistence of infinitely many KLUS-simple Newhouse attracting sets

DOI10.1007/BF02099177zbMath0752.58019OpenAlexW2013601145MaRDI QIDQ1189232

Helena E. Nusse, Laura Tedeschini Lalli

Publication date: 26 September 1992

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099177

zbMATH Keywords

diffeomorphismsaddlehomoclinic point

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Dynamical systems with hyperbolic behavior (37D99)

Related Items (5)

How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency ⋮ A period-doubling cascade precedes chaos for planar maps ⋮ Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces ⋮ Feigenbaum networks ⋮ Bifurcation rigidity

Cites Work

• Bifurcation to infinitely many sinks
• The Newhouse set has a positive Hausdorff dimension
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Period doubling cascades of attractors: A prerequisite for horseshoes
• How often do simple dynamical processes have infinitely many coexisting sinks?
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Diffeomorphisms with infinitely many sinks
• Bifurcations of one- and two-dimensional maps
• Asymptotically Periodic Behaviour in the Dynamics of Chaotic Mappings
• Analysis of a procedure for finding numerical trajectories close to chaotic saddle hyperbolic sets
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