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Symbolic dynamics and the discrete variational principle

H R Dullin

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We show how to construct symbolic dynamics for the class of 2d-dimensional twist mappings generated by piecewise strictly convex/concave generating functions. The method is constructive and gives an efficient way to find all periodic orbits of these high-dimensional symplectic mappings. It is illustrated with the cardioid and the stadium billiard.


PACS

02.30.Jr Partial differential equations

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

MSC

37E40 Twist maps

37K05 Hamiltonian structures, symmetries, variational principles, conservation laws

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 45 (13 November 1998)

Received 24 March 1998, in final form 14 August 1998



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