On a certain class of linear Hamiltonian maps

Otsuki, Nobukazu; Suzuki, Sintaro

doi:10.1090/S0002-9939-06-08370-5

On a certain class of linear Hamiltonian maps
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by Nobukazu Otsuki and Sintaro Suzuki PDF

Proc. Amer. Math. Soc. 134 (2006), 3637-3644 Request permission

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

Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. MR 515141
Helmut Hofer and Eduard Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 1994. MR 1306732, DOI 10.1007/978-3-0348-8540-9
Jürgen Moser, Monotone twist mappings and the calculus of variations, Ergodic Theory Dynam. Systems 6 (1986), no. 3, 401–413. MR 863203, DOI 10.1017/S0143385700003588
Dusa McDuff and Dietmar Salamon, Introduction to symplectic topology, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. Oxford Science Publications. MR 1373431
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.
Sintaro Suzuki, Moser’s construction of time-dependent Hamiltonian function which defines a Hamiltonian map on $\Bbb R^{2n}$, SUT J. Math. 39 (2003), no. 1, 105–116. MR 1993843