Convergence of Hamiltonian systems to billiards

Chaos

Volumn 8, Issue 2, 1998, Pages 466-474

  Collas, Peter ^a   Klein, David ^a   Schwebler, Hans Peter ^b  

^a CALIFORNIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041192959     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166328     Document Type: Article

References (12)

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2. V. V. Kozlov and D. V. Treshchëv, Billiards. A Genetic Introduction to the Dynamics of Systems with Impacts (American Mathematical Society translations of Mathematical Monographs Vol. 89, Providence, Rhode Island, 1991).
3. P. Dahlqvist and G. Russberg, "Periodic orbit quantization of bound chaotic systems," J. Phys. A 24, 4763-4778 (1991); for example, Ref. 28, p. 687 in Pikovsky et al. Chaos 7, 680 (1997).
4. P. Dahlqvist and G. Russberg, "Periodic orbit quantization of bound chaotic systems," J. Phys. A 24, 4763-4778 (1991); for example, Ref. 28, p. 687 in Pikovsky et al. Chaos 7, 680 (1997).
5. H. Yoshida, "A type of second order linear ordinary differential equations with periodic coefficients for which the characteristic exponents have exact expressions," Celest. Mech. 32, 73-86 (1984).
6. H. Yoshida, "Existence of exponentially unstable periodic solutions and the nonintegrability of homogeneous Hamiltonian systems," Physica D 21, 163-170 (1986).
7. H. Yoshida, "A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential," Physica D 29, 128-142 (1987).
8. L. D. Landau and E. M. Lifshitz, Mechanics, 3rd ed. (Butterworth-Heinemann, Oxford, 1976), p. 22.
9. M. V. Berry, "Regularity and chaos in classical mechanics, illustrated by three deformations of a circular billiard," Eur. J. Phys. 2, 91-102 (1981).
10. S. L. Ziglin, "Branching of solutions and non-existence of first integrals in Hamiltonian mechanics I," Funct. Anal. Appl. 16, 181-189 (1983); "Branching of solutions and non-existence of first integrals in Hamiltonian mechanics II," ibid. 17, 6-17 (1983).
11. S. L. Ziglin, "Branching of solutions and non-existence of first integrals in Hamiltonian mechanics I," Funct. Anal. Appl. 16, 181-189 (1983); "Branching of solutions and non-existence of first integrals in Hamiltonian mechanics II," ibid. 17, 6-17 (1983).
12. A. Ramani, B. Dorizzi, and B. Grammaticos, "Painlevé conjecture revisited," Phys. Rev. Lett. 49, 1539-1541 (1982).