An exhaustive criterion for the non-existence of invariant circles for area-preserving twist maps

DOI10.1007/BF01223588zbMath0666.58040OpenAlexW2046523287MaRDI QIDQ1116514

Jaroslav Stark

Publication date: 1988

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01223588

zbMATH Keywords

area-preserving twist mapconefieldrotational invariant circle

Mathematics Subject Classification ID

Dynamical systems and ergodic theory (37-XX)

Related Items (10)

Regions without invariant tori of given class for the planar circular restricted three-body problem ⋮ Jaroslav Stark: 1960–2010 ⋮ Computation of the breakdown of analyticity in statistical mechanics models: Numerical results and a renormalization group explanation ⋮ A criterion for non-existence of invariant tori for Hamiltonian systems ⋮ Using integrability to produce chaos: Billiards with positive entropy ⋮ Non-integrability of measure preserving maps via Lie symmetries ⋮ Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow ⋮ Accurate strategies for small divisor problems ⋮ Regions of nonexistence of invariant tori for spin-orbit models ⋮ Converse KAM: theory and practice

Cites Work

• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Definite paths and upper bounds on regular regions of velocity phase space
• A renormalization approach to invariant circles in area-preserving maps
• Converse KAM: theory and practice
• Transport in Hamiltonian systems
• A criterion for the non-existence of invariant circles
• Boundary circles for area-preserving maps
• Invariant circles and the order structure of periodic orbits in monotone twist maps
• Non-existence of invariant circles
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