Topological methods in the instability problem of Hamiltonian systems
From MaRDI portal
Publication:2496406
DOI10.3934/dcds.2006.14.295zbMath1098.37056OpenAlexW2150429134MaRDI QIDQ2496406
Rafael de la Llave, Marian Gidea
Publication date: 6 July 2006
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcds.2006.14.295
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Nearly integrable Hamiltonian systems, KAM theory (70H08)
Related Items
Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion, Arnold diffusion in a priori chaotic symplectic maps, Arnold diffusion of charged particles in ABC magnetic fields, Topological shadowing methods in arnold diffusion: weak torsion and multiple time scales, A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems, Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the <scp>Three‐Body</scp> Problem, A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes, A geometric mechanism of diffusion: rigorous verification in a priori unstable Hamiltonian systems, Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies, Global diffusion on a tight three-sphere, Morse-type inequalities for dynamical systems and the Witten Laplacian, The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks, Hyperbolicity versus partial-hyperbolicity and the transversality-torsion phenomenon, Global instability in the restricted planar elliptic three body problem, Geometric properties of the scattering map of a normally hyperbolic invariant manifold, Perturbations of geodesic flows by recurrent dynamics, An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension, Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument, A \(\lambda\)-lemma for normally hyperbolic invariant manifolds, Covering relations, cone conditions and the stable manifold theorem, Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio, Diffusing orbits along chains of cylinders