Metamorphoses: Sudden jumps in basin boundaries

DOI10.1007/BF02100002zbMath0746.58053OpenAlexW2112188828MaRDI QIDQ1182046

James A. Yorke, Kathleen T. Alligood, Laura Tedeschini Lalli

Publication date: 27 June 1992

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

Full work available at URL: https://doi.org/10.1007/bf02100002

zbMATH Keywords

homoclinic tangencyiterated mapsbasic of attractionbasin boundary metamorphoseshorseshoe mapsNewhouse saddles

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems with hyperbolic behavior (37D99)

Related Items

A special type of explosion of basin boundary ⋮ Optimal escape from potential wells -- patterns of regular and chaotic bifurcation ⋮ Backbones in the parameter plane of the Hénon map ⋮ Accessible saddles on fractal basin boundaries ⋮ A dynamical interpretation of sequential decay in reactive scattering ⋮ Strange nonchaotic attractors with Wada basins ⋮ On detachable maps and flows ⋮ Basin reversal in nonlinear driven oscillators ⋮ Boundary crisis in quasiperiodically forced systems ⋮ Boundary crisis bifurcation in two parameters ⋮ Explosions of chaotic sets ⋮ Outer Tangency Bifurcations of Chaotic Sets ⋮ Rotation numbers of periodic orbits in the Hénon map

Cites Work

• Bifurcation to infinitely many sinks
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• How often do simple dynamical processes have infinitely many coexisting sinks?
• Jumping stable manifolds for dissipative maps of the plane
• Basin boundary metamorphoses: Changes in accessible boundary orbits
• Diffeomorphisms with infinitely many sinks
• Differentiable dynamical systems
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I