Non-existence of invariant circles

DOI10.1017/S0143385700002455zbMath0557.58019MaRDI QIDQ3221077

John N. Mather

Publication date: 1984

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

dynamical systemdifference equationinvariant circles

Mathematics Subject Classification ID

Dynamical systems with hyperbolic behavior (37D99)

Related Items (47)

A criterion for the non-existence of invariant circles ⋮ An obstruction method for the destruction of invariant curves ⋮ Invariant circles and rotation bands in monotone twist maps ⋮ The existence of gaps in minimal foliations ⋮ Escape times across the golden cantorus of the standard map ⋮ Analysis of the separatrix map in Hamiltonian systems ⋮ Construction of analytic KAM-surfaces and effective stability bounds ⋮ Critical dynamics and trees ⋮ Quasi-periodic solutions of nonlinear elliptic partial differential equations ⋮ An exhaustive criterion for the non-existence of invariant circles for area-preserving twist maps ⋮ Equatorial dynamics of charged particles in planetary magnetospheres ⋮ Diffusion and chaos in a bouncing ball model ⋮ Efficient and reliable algorithms for the computation of non-twist invariant circles ⋮ Rigorous computer-assisted application of KAM theory: a modern approach ⋮ Isodrastic magnetic fields for suppressing transitions in guiding-centre motion ⋮ Some questions looking for answers in dynamical systems ⋮ Rotation sets and Morse decompositions in twist maps ⋮ On the fragility of periodic tori for families of symplectic twist maps ⋮ Combination laws for scaling exponents and relation to the geometry of renormalization operators ⋮ A pioneer of chaos ⋮ A criterion for non-existence of invariant tori for Hamiltonian systems ⋮ Analysis of resonances in the spin-orbit problem in celestial mechanics. I: The synchronous resonance ⋮ Unnamed Item ⋮ On the regularity of Mather's \(\beta\)-function for standard-like twist maps ⋮ Width of stochastic layers in near-integrable two-dimensional symplectic maps. ⋮ Stability of homoclinic orbits and diffusion in phase space. ⋮ Using integrability to produce chaos: Billiards with positive entropy ⋮ Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow ⋮ Stable and unstable manifolds asymptotic to the outermost KAM curve ⋮ Gevrey-smoothness of lower dimensional hyperbolic invariant tori for nearly integrable symplectic mappings ⋮ Exact numerical studies of Hamiltonian maps: Iterating without roundoff error ⋮ A rigorous partial justification of Greene's criterion ⋮ Natural boundaries for area-preserving twist maps ⋮ Ground states and critical points for Aubry-Mather theory in Statistical mechanics ⋮ Renormalization for golden circles ⋮ Unnamed Item ⋮ Amount of rotation about a point and the Morse index ⋮ Nonexistence of invariant tori transverse to foliations: An application of converse KAM theory ⋮ Invariant curves for area-preserving twist maps far from integrable ⋮ Destruction of invariant circles ⋮ A quantitative rigidity result for a two-dimensional Frenkel-Kontorova model ⋮ Effect of islands in diffusive properties of the standard map for large parameter values ⋮ Diffusing orbits along chains of cylinders ⋮ Breakup of invariant tori for the four-dimensional semi-standard map ⋮ On a result by J. N. Mather concerning invariant sets for area-preserving twist maps ⋮ Hamiltonian systems, Lagrangian tori and Birkhoff's theorem ⋮ Converse KAM: theory and practice

Cites Work

• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION

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