@Article{ATA-37-1,
author = {Sergey, Bolotin},
title = {Shadowing Homoclinic Chains to a Symplectic Critical Manifold},
journal = {Analysis in Theory and Applications},
year = {2021},
volume = {37},
number = {1},
pages = {1--23},
abstract = {<p style="text-align: justify;">We prove the existence of trajectories&nbsp; 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&nbsp; degree of freedom and a figure 8 separatrix.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2021.pr80.11},
url = {https://global-sci.com/article/73775/shadowing-homoclinic-chains-to-a-symplectic-critical-manifold}
}