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On a certain class of linear Hamiltonian maps

Author(s): Nobukazu Otsuki; Sintaro Suzuki
Journal: Proc. Amer. Math. Soc. 134 (2006), 3637-3644.
MSC (2000): Primary 53D22, 70H15
Posted: June 15, 2006
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Abstract: We discovered a certain class of linear Hamiltonian maps which are defined by explicit time dependent Hamiltonian functions. Our method is the analogy of Moser's construction in 1986, although it is not so difficult, but we think the results are new.

References:

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R. Abraham and J. Marsden, Foundations of Mechanics, Second edition. Addison-Wesley, Reading, 1978. MR 0515141 (81e:58025)

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H. Hofer and E. Zehnder, Symplectic Invariants and Hamiltonian Dynamics, Birkhauser, Basel, 1994. MR 1306732 (96g:58001)

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J. Moser, Monotone twist mappings and the calculus of variations, Ergod. Th. & Dynam. Sys. 6 (1986) 401-413. MR 0863203 (88a:58076)

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D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford Univ. Press, 1995. MR 1373431 (97b:58062)

[OS]
N. Otsuki and S. Suzuki, Monotone twist maps on $ T^{*}\mathbb{T}^{n}$ and Mather's theory for minimal measures, submitted to Ergodic Theory and Dynamical Systems.

[Su]
S. Suzuki, Moser's construction of time-dependent Hamiltonian function which defines a Hamiltonian map on $ \mathbb{R}^{2n}$, SUT. J. Math. 39 (2003) 105-116. MR 1993843 (2005b:37115)

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Additional Information:

Nobukazu Otsuki
Affiliation: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba(278-8510), Japan
Email: otsuki_nobukazu@ma.noda.tus.ac.jp

Sintaro Suzuki
Affiliation: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba(278-8510), Japan
Email: suzuki_sintaro@ma.noda.tus.ac.jp

DOI: 10.1090/S0002-9939-06-08370-5
PII: S 0002-9939(06)08370-5
Keywords: Hamiltonian map, Hamiltonian function
Received by editor(s): May 17, 2004
Received by editor(s) in revised form: June 10, 2005
Posted: June 15, 2006
Communicated by: Carmen C. Chicone
Copyright of article: Copyright 2006, American Mathematical Society

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