Numerical Computation of Critical Surfaces for the Breakup of Invariant Tori in Hamiltonian Systems

DOI10.1137/21M1448501MaRDI QIDQ5887856

Adrián P. Bustamante, Cristel Chandre

Publication date: 14 April 2023

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

Full work available at URL: https://arxiv.org/abs/2109.12235

zbMATH Keywords

Hamiltonian systemsrenormalizationinvariant toriKAM

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Uses Software

• SciPy
• NumPy
• Python

Cites Work

• The parameterization method for invariant manifolds. From rigorous results to effective computations
• Computation of the breakdown of analyticity in statistical mechanics models: Numerical results and a renormalization group explanation
• Construction of analytic KAM-surfaces and effective stability bounds
• Break-up of the spiral mean torus in a volume-preserving map
• Renormalization-group analysis for the transition to chaos in Hamiltonian systems
• KAM theory in configuration space
• Greene's residue criterion for the breakup of invariant tori of volume-preserving maps
• The analyticity breakdown for Frenkel-Kontorova models in quasi-periodic media: numerical explorations
• Birkhoff averages and rotational invariant circles for area-preserving maps
• Fast numerical computation of quasi-periodic equilibrium states in 1D statistical mechanics, including twist maps
• A renormalization group for Hamiltonians: numerical results
• A renormalization group for Hamiltonians, with applications to KAM tori
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Super convergence of ergodic averages for quasiperiodic orbits
• KAM Theory for Quasi-periodic Equilibria in One-Dimensional Quasi-periodic Media
• Improved estimates on the existence of invariant tori for Hamiltonian systems
• Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems

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