@Article{ATA-37-1, author = {Bolotin , Sergey}, 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 = {

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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2021.pr80.11}, url = {http://global-sci.org/intro/article_detail/ata/18762.html} }