Multiple separatrix crossing in multi-degree-of freedom Hamiltonian flows: Global geometry and phase space transport associated with multiple partial barriers and turnstiles
Center for Theory and Simulation in Science and Engineering, Cornell University, 1994 - Mathematics - 72 pages
15 pages matching Melnikov theory in this book
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2D maps 2D slice analysis Arnold diffusion asymptotic analysis asymptotically approach Beigie bounded and unbounded codimension-one invariant manifolds codimension-one manifolds codimension-one partitioning codimension-one separatrix codimension-one stable codimension-one surface component context critical asymptotic behavior defined degree-of-freedom denotes distance function dividing surface E2crit energy surface equation G R2 geometry associated global bifurcation global stable Hamiltonian systems Hence hyperbolic fixed point hyperbolic invariant manifolds ifolds initial condition invariant manifold geometry level set libration Lyapunov exponent manifold W'(M Melnikov theory Melnikov zero set Morse oscillators Morse-Morse coupling near-integrable normally hyperbolic invariant parametrized partially destroyed separatrix partitioning and transport partitioning surface persistence and smoothness phase space partitioning phase space transport Poincare map Poincare section pre-image qualitatively different dynamics regions of qualitatively segments of stable separation profiles single-separatrix solution stable and unstable tonian trajectory transition transport theory turnstile boundaries turnstile lobe unbounded motion unperturbed flow unperturbed phase portrait unperturbed separatrix unstable manifolds vector field Wiggins