Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori

DOI10.1016/S0167-2789(98)90020-3zbMath0664.58032OpenAlexW1974286907MaRDI QIDQ1114977

Robert S. MacKay

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/s0167-2789(98)90020-3

zbMATH Keywords

orbitsHamiltonian systemsstable manifoldsunstable manifoldsfree semi-grouprenormalisation schemeuniversal fractal diagrams

Mathematics Subject Classification ID

Topological dynamics (37B99) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (16)

Boundary circles for area-preserving maps ⋮ Modular smoothing and KAM tori ⋮ Universal small-scale structure near the boundary of Siegel disks of arbitrary rotation number ⋮ Regions without invariant tori of given class for the planar circular restricted three-body problem ⋮ A convergence criterion for the unstable manifolds of the MacKay approximate renormalisation ⋮ Renormalization-group analysis for the transition to chaos in Hamiltonian systems ⋮ On Slater's criterion for the breakup of invariant curves ⋮ Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori ⋮ Regularity properties of \(k\)-Brjuno and Wilton functions ⋮ Fractal boundary for the existence of invariant circles for area- preserving maps: Observations and renormalisation explanation ⋮ An approximate renormalization for the break-up of invariant tori with three frequencies ⋮ Critical function for the standard map ⋮ Approximate renormalization with codimension-one fixed point for the break-up of some three-frequency tori ⋮ Renormalization of Aubry-Mather Cantor sets ⋮ Unstable manifolds for the MacKay approximate renormalisation ⋮ Diffusion and scaling in escapes from two-degrees-of-freedom Hamiltonian systems

Cites Work

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• Boundary circles for area-preserving maps
• Universal small-scale structure near the boundary of Siegel disks of arbitrary rotation number
• 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
• Unstable manifolds for the MacKay approximate renormalisation
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Existence, nonexistence and universal breakdown of dissipative golden invariant tori. I. Golden critical circle maps
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• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

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