Multiple Separatrix Crossing in Multi-degree-of Freedom Hamiltonian Flows: Global Geometry and Phase Space Transport Associated with Multiple Partial Barriers and TurnstilesCenter for Theory and Simulation in Science and Engineering, Cornell University, 1994 - Hamiltonian systems - 72 pages |
Common terms and phrases
2D maps 2D slice analysis Arnold diffusion asymptotic analysis asymptotically approach Beigie bounded and unbounded codimension-one invariant manifolds codimension-one partitioning codimension-one separatrix codimension-one stable codimension-two context defined degree-of-freedom denotes distance function dividing surface E₁ E₂ E2erit energy surface equation Figure geometry associated global stable Hamiltonian flows Hamiltonian systems Hence hyperbolic fixed point hyperbolic invariant manifolds ifolds initial condition invariant manifold geometry level set Melnikov theory Melnikov zero set Morse oscillators Morse-Morse coupling near-integrable normally hyperbolic invariant numerical computation parametrized partial barriers partially destroyed separatrix partitioning and transport partitioning surface persistence and smoothness phase space partitioning phase space transport Poincaré map Poincaré section pre-image qualitatively different dynamics r₂ regions of qualitatively segments of stable separation profiles single-separatrix solution stable and unstable to₁ to₂ trajectory transition transport theory turnstile boundaries turnstile lobe unbounded motion unperturbed flow unperturbed phase portrait unperturbed separatrix unstable manifolds vector field Wiggins