By Hans Jürgen Korsch; Hansjörg Jodl; Timo Hartmann
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Extra resources for Chaos : a program collection for the PC; with many numerical experiments and a CD-ROM
50 3 Billiard Systems Fig. 3. Circular billiard: Five periodic orbits and a non-periodic one. 1 Deformations of a Circle Billiard It is instructive to discuss the simplest billiard form, the circle, and some of its deformations in some detail: (a) Circle: This is the simplest form of a boundary curve. , as a special case of an ellipse. The system is rotationally symmetric and, therefore, integrable as a consequence of the existence of a second constant of motion in addition to the energy, namely, the angular momentum.
Cvitanovi´c, Universality in Chaos, Adam Hilger, Bristol, 1984 11. R. S. MacKay and J. D. Meiss, Hamiltonian Dynamical Systems, Adam Hilger, Bristol, 1987 12. D. Ruelle, Strange attractors, Math. Intelligencer 2 (1980) 126, reprinted in: P. Cvitanovi´c, Universality in Chaos, Adam Hilger, Bristol, 1984 46 2 Nonlinear Dynamics and Deterministic Chaos 13. S. Smale, Diﬀeomorphisms with many periodic points, in S. S. Cairns, editor, Diﬀerential and Combinatorial Topology. Princeton University Press, Princeton, 1963 14.
Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20 (1971) 167, reprinted in: Hao Bai-Lin, Chaos, World Scientiﬁc, Singapore, 1984 15. S. E. Newhouse, D. Ruelle, and F. Takens, Occurrence of strange axiom A attractors near quasiperiodic ﬂows on T m , m ≥ 3, Commun. Math. Phys. 64 (1978) 35 16. P. Manneville and Y. Pomeau, Intermittency and the Lorenz model, Phys. Lett. A 75 (1979) 1 17. Y. Pomeau and P. Manneville, Intermittent transition to turbulence in dissipative dynamical systems, Commun.
Chaos : a program collection for the PC; with many numerical experiments and a CD-ROM by Hans Jürgen Korsch; Hansjörg Jodl; Timo Hartmann