Erratic behavior of invariant circles in standard-like mappings

DOI10.1016/0167-2789(87)90235-1zbMath0612.58021OpenAlexW2058877665MaRDI QIDQ1088227

Jacob Wilbrink

Publication date: 1987

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90235-1

zbMATH Keywords

KAM torusmappings like the standard map

Mathematics Subject Classification ID

Topological dynamics (37B99) Iteration of real functions in one variable (26A18)

Related Items

Renormalization and transition to chaos in area preserving nontwist maps ⋮ Area preserving nontwist maps: Periodic orbits and transition to chaos ⋮ Renormalisation in implicit complex maps ⋮ Fractal boundary for the existence of invariant circles for area- preserving maps: Observations and renormalisation explanation ⋮ Subdiffusive transport in stochastic webs ⋮ Recurrence of Kolmogorov-Arnold-Moser tori in nonanalytic twist maps ⋮ A rigorous partial justification of Greene's criterion ⋮ Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors ⋮ A renormalization group explanation of numerical observations of analyticity domains ⋮ What makes chaos border sticky? ⋮ Critical invariant circles in asymmetric and multiharmonic generalized standard maps ⋮ Breakdown of Lindstedt expansion for chaotic maps

Cites Work

• Unnamed Item
• Universal behaviour in families of area-preserving maps
• Hamiltonian maps in the complex plane
• A renormalization approach to invariant circles in area-preserving maps
• Converse KAM: theory and practice
• Critical Behavior of a KAM surface. I: Empirical results
• Invariant circles for the piecewise linear standard map
• Analytic results for the scaling behaviour of a piecewise-linear map of the circle