Classification of perturbations of Diophantine \(\mathbb{Z}^m\) actions on tori of arbitrary dimension

DOI10.1134/S1560354721060083zbMath1490.37085OpenAlexW4200387744MaRDI QIDQ2074776

Boris Petković

Publication date: 10 February 2022

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354721060083

zbMATH Keywords

KAM theorylocal rigiditysimultaneously Diophantine approximationssimultaneously Diophantine translations

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

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On simultaneous linearization of certain commuting nearly integrable diffeomorphisms of the cylinder ⋮ Transversal local rigidity of discrete abelian actions on Heisenberg nilmanifolds

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