Shadowing Homoclinic Chains to a Symplectic Critical Manifold  

作　　者：Sergey Bolotin 

机构地区：[1]Moscow Steklov Mathematical Institute,Russian Academy of Sciences,Moscow,119991,Russia

出　　处：《Analysis in Theory and Applications》2021年第1期1-23,共23页分析理论与应用（英文刊）

基　　金：This work is supported by the Russian Science Foundation under grant No.19-71-30012.

摘　　要：We prove the existence of trajectories shadowing chains of heteroclinic or-bits to a sy mplectic normally hyperbolic critical manifold of a Hamiltonian system.The results are quite different for real and complex eigenvalues.General results are applied to Hamitonian systems depending on a parameter which slowly changes with rateε.If the frozen autonomous system has a hyperbolic equilibrium possessing trans-verse homoclinic orbits,we construct trajectories shadowing homoclinic chains with energy having quasirandom jumps of orderεand changing with average rate of orderε|lnε|.This provides a partial multidimensional extension of the results of A.Neish-tadt on the destruction of adiabatic invariants for systems with one degree of freedom and a figure 8 separatrix.

关 键 词：Hamiltonian system homoclinic orbit SHADOWING 

分 类 号：O186.1[理学—数学]