Fractal boundary for the existence of invariant circles for area- preserving maps: Observations and renormalisation explanation

DOI10.1016/0167-2789(89)90073-0zbMath0696.58032OpenAlexW2047873338MaRDI QIDQ910784

Robert S. MacKay, Jukka A. Ketoja

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0167-2789(89)90073-0

zbMATH Keywords

critical linearea-preserving mapinvariant circle

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (16)

Cantori for multiharmonic maps ⋮ Renormalization and transition to chaos in area preserving nontwist maps ⋮ Nonanalytic twist maps and Frenkel-Kontorova models ⋮ Rotationally-ordered periodic orbits for multiharmonic area-preserving twist maps ⋮ Area preserving nontwist maps: Periodic orbits and transition to chaos ⋮ Some questions looking for answers in dynamical systems ⋮ Recurrence of Kolmogorov-Arnold-Moser tori in nonanalytic twist maps ⋮ Break-up of the spiral mean torus in a volume-preserving map ⋮ Circle maps with symmetry-breaking perturbations ⋮ 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 ⋮ Breakup of inverse golden mean shearless tori in the two-frequency standard nontwist map ⋮ Critical invariant circles in asymmetric and multiharmonic generalized standard maps ⋮ Global dynamics and diffusion in the rational standard map ⋮ Rigorous chaos verification in discrete dynamical systems

Cites Work

• Unnamed Item
• Unnamed Item
• A renormalization approach to invariant circles in area-preserving maps
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Transport in Hamiltonian systems
• Erratic behavior of invariant circles in standard-like mappings
• Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori
• Critical Behavior of a KAM surface. I: Empirical results
• Period doubling for bimodal maps: a horseshoe for a renormalisation operator
• Locally most robust circles and boundary circles for area-preserving maps

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