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Russian Mathematical Surveys, 2007, Volume 62, Issue 2, Pages 219–322
DOI: https://doi.org/10.1070/RM2007v062n02ABEH004396 (Mi rm6804) 		 
This article is cited in 36 scientific papers (total in 36 papers)

Separatrix maps in Hamiltonian systems

G. N. Piftankina, D. V. Treschevb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (1354 kB) Citations (36)
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DOI: https://doi.org/10.1070/RM2007v062n02ABEH004396
Abstract: The separatrix map is constructed for some classes of problems in Hamiltonian dynamics. The formulae obtained are used to study two-dimensional symplectic maps close to integrable maps: elliptic periodic trajectories passing through separatrix lobes are constructed, and some estimates for the width of the stochastic layer are given. For Hamiltonian systems with two and a half degrees of freedom it is proved that the Arnol'd diffusion in the a priori unstable case is generic, and in the Mather problem trajectories are constructed for which the mean energy growth is linear in time.
Received: 01.02.2007
Russian version:
Uspekhi Matematicheskikh Nauk, 2007, Volume 62, Issue 2(374), Pages 3–108
DOI: https://doi.org/10.4213/rm6804
Bibliographic databases:
Document Type: Article
UDC: 531.01
MSC: Primary 37J40, 37J10; Secondary 34C37, 37J45, 37D10, 37D30, 37C55, 70H05
Language: English
Original paper language: Russian
Citation: G. N. Piftankin, D. V. Treschev, “Separatrix maps in Hamiltonian systems”, Uspekhi Mat. Nauk, 62:2(374) (2007), 3–108; Russian Math. Surveys, 62:2 (2007), 219–322
Citation in format AMSBIB
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    • This publication is cited in the following 36 articles:
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