Regularity Properties of Critical Invariant Circles of Twist Maps, and Their Universality

DOI10.1137/070687967zbMath1159.37314arXivnlin/0609024OpenAlexW1985764914MaRDI QIDQ3624475

Arturo Olvera, Nikola P. Petrov

Publication date: 30 April 2009

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0609024

zbMATH Keywords

Fourier analysisuniversalitytwist mapsregularity of functionscritical invariant circles

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Universality and renormalization of dynamical systems (37E20) Dynamical aspects of twist maps (37E40)

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Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map ⋮ Rigorous computer-assisted application of KAM theory: a modern approach ⋮ Combination laws for scaling exponents and relation to the geometry of renormalization operators ⋮ A new method to compute periodic orbits in general symplectic maps ⋮ Critical invariant circles in asymmetric and multiharmonic generalized standard maps ⋮ Numerical computation of rotation numbers of quasi-periodic planar curves ⋮ Boundaries of Siegel disks: Numerical studies of their dynamics and regularity

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