Year: 2021
Author: Sergey Bolotin
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 1–23
Abstract
We prove the existence of trajectories shadowing chains of heteroclinic orbits to a symplectic normally hyperbolic critical manifold of a Hamiltonian system. The results are quite different for real and complex eigenvalues. General results are applied to Hamiltonian systems depending on a parameter which slowly changes with rate $\varepsilon$. If the frozen autonomous system has a hyperbolic equilibrium possessing transverse homoclinic orbits, we construct trajectories shadowing homoclinic chains with energy having quasirandom jumps of order $\varepsilon$ and changing with average rate of order $\varepsilon|\ln\varepsilon|$. This provides a partial multidimensional extension of the results of A. Neishtadt on the destruction of adiabatic invariants for systems with one degree of freedom and a figure 8 separatrix.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2021.pr80.11
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 1–23
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Hamiltonian system homoclinic orbit shadowing.
Author Details
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