Dmitry Turaev and Vered Rom-Kedar 1998 Nonlinearity 11 575 doi:10.1088/0951-7715/11/3/010
Dmitry Turaev and Vered Rom-Kedar
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It is proved that periodic and homoclinic trajectories which are tangent to the boundary of any scattering (ergodic) billiard produce elliptic islands in the `nearby' Hamiltonian flows i.e. in a family of two-degrees-of-freedom smooth Hamiltonian flows which converge to the singular billiard flow smoothly where the billiard flow is smooth and continuously where it is continuous. Such Hamiltonians exist; indeed, sufficient conditions are supplied, and thus it is proved that a large class of smooth Hamiltonians converges to billiard flows in this manner. These results imply that ergodicity may be lost in the physical setting, where smooth Hamiltonians which are arbitrarily close to the ergodic billiards, arise.
05.45.-a Nonlinear dynamics and nonlinear dynamical systems
45.50.-j Dynamics and kinematics of a particle and a system of particles
70Fxx Dynamics of a system of particles, including celestial mechanics
34C37 Homoclinic and heteroclinic solutions
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
Issue 3 (May 1998)
Received 8 September 1997, in final form 22 January 1998
Dmitry Turaev and Vered Rom-Kedar 1998 Nonlinearity 11 575
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