Geodesic
Separatrix Maps in Slow--Fast Hamiltonian Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern Methods of Mechanics, Tome 322 (2023), pp. 38-57

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We obtain explicit formulas for the separatrix map of a multidimensional slow–fast Hamiltonian system. This map is used to partly extend Neishtadt's results on the jumps of adiabatic invariants at the separatrix to the multidimensional case.
Keywords: slow–fast system, Poincaré function, separatrix map
Mots-clés : homoclinic orbit, adiabatic invariant. 
@article{TM_2023_322_a3,
     author = {Sergey V. Bolotin},
     title = {Separatrix {Maps} in {Slow--Fast} {Hamiltonian} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {38--57},
     publisher = {mathdoc},
     volume = {322},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2023_322_a3/}
}
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Sergey V. Bolotin. Separatrix Maps in Slow--Fast Hamiltonian Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern Methods of Mechanics, Tome 322 (2023), pp. 38-57. http://geodesic.mathdoc.fr/item/TM_2023_322_a3/