TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
From MaRDI portal
Publication:4301190
DOI10.1142/S0129055X9400016XzbMath0798.58036arXivchao-dyn/9304012MaRDI QIDQ4301190
Publication date: 3 November 1994
Published in: Reviews in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/chao-dyn/9304012
perturbation theoryrenormalizationKAM theoryhomoclinic pointsclassical mechanicscancellationscompletely integrable Hamiltonian systems
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)
Related Items
MEL'NIKOV'S APPROXIMATION DOMINANCE: SOME EXAMPLES, KAM theory near multiplicity one resonant surfaces in perturbations of a-priori stable Hamiltonian systems, On the conservation of adiabatic invariants for a system of coupled rotators, Exponentially Small Splitting and Arnold Diffusion for Multiple Time Scale Systems, Compensations in small divisor problems, A note on quasi-periodic solutions of some elliptic systems, Fast drift and diffusion in a class of isochronous systems with the windows method, Exponentially small splitting for the pendulum: A classical problem revisited, Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio, CONSTRUCTION OF WHISKERS FOR THE QUASIPERIODICALLY FORCED PENDULUM, Majorant series convergence for twistless KAM tori, Kolmogorov algorithm for isochronous Hamiltonian systems, Kolmogorov variation: Kam with knobs \textit{(à la Kolmogorov)}, Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing, Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems, A RENORMALIZATION PROOF OF THE KAM THEOREM FOR NON-ANALYTIC PERTURBATIONS, On homoclinic splitting problems, A new method for measuring the splitting of invariant manifolds, Constructive field theory and applications: Perspectives and open problems, Frequency locking in an injection-locked frequency divider equation, Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results, Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows., Renormalization group in statistical mechanics and mechanics: gauge symmetries and vanishing beta functions, Unnamed Item, Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence, A version of Thirring’s approach to the Kolmogorov–Arnold–Moser theorem for quadratic Hamiltonians with degenerate twist, The KAM theorem and renormalization group, Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio, Universal homoclinic bifurcations and chaos near double resonances, An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum, Degenerate elliptic resonances, A field theory approach to Lindstedt series for hyperbolic tori in three time scales problems, Fractional Lindstedt series, Kato perturbative expansion in classical mechanics and an explicit expression for the Deprit generator
