|
|
|
|
References
|
|
| |
| 1. |
M. Bialy, “Convex billiards and a theorem by E. Hopf”, Math. Z., 214:1 (1993), 147–154    |
| 2. |
I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai, Ergodic Theory, Springer Verlag, 1982 |
| 3. |
A. Delshams, R. Ramírez-Ros, “Poincare–Melnikov–Arnold method for analytic planar maps”, Nonlinearity, 9:1 (1996), 1–26  |
| 4. |
A. Delshams, R. Ramírez-Ros, “On Birkhoff's conjecture about convex billiards”, Proceedings of the 2nd Catalan Days on Applied Mathematics (Odeillo, 1995), Collect. Études, Presses Univ. Perpignan, 1995, 85–94 |
| 5. |
V. J. Donnay, “Using integrability to produce chaos: billiards with positive entropy”, Comm. Math. Phys., 141 (1991), 225–257 |
| 6. |
V. J. Donnay, “Transverse homoclinic connections for geodesic flows”, Hamiltonian dynamical systems (Cincinnati, OH, 1992), IMA Vol. Math. Appl., 63, Springer, New York, 1995, 115–125 |
| 7. |
M. M. Dvorin, V. F. Lazutkin, “Existence of an infinite number of elliptic and hyperbolic periodic
trajectories for convex billiards”, Funk. Anal. Priloz., 7:2 (1973), 20–27  |
| 8. |
V. Gelfreich, “A century of separatrices splitting in Hamiltonian dynamical systems:
perturbation theory, exponential smallness”, XIII International Congress on Mathematical Physics, Int. Press, Boston, MA, London, 2000, 73–86 |
| 9. |
V. Gelfreich, V. F. Lazutkin, “Splitting of separatrices: perturbation theory and exponential smallness”, Uspekhi Mat. Nauk, 56:3(339) (2001), 79–142 |
| 10. |
N. Innami, “Geometry of geodesics for convex billiards and circular billiards”, Nihonkai Math. J., 13:1 (2002), 73–120 |
| 11. |
Gwang Il Kim, “Elliptic Birkhoff's billiards with $C^2$-generic global perturbations”, Bull. Korean Math. Soc., 36:1 (1999), 147–159 |
| 12. |
G. Knieper, H. Weiss, “A surface with positive curvature and positive topological entropy”, J. Differential Geom., 39:2 (1994), 229–249 |
| 13. |
H. E. Lomeli, “Perturbations of elliptic billiards”, Phys. D, 99:1 (1996), 59–80 |
| 14. |
G. Paternain, “Real analytic convex surfaces with positive topological entropy and
rigid body dynamics”, Manuscripta Math., 78:4 (1993), 397–402 |
| 15. |
D. Petroll, Existenz und Transversalitt von Homoklinen und Heteroklinen Orbits
beim Geodtischen Fluss, Thesis, Universitt Freiburg, 1996 |
| 16. |
Ya. G. Sinai, Introduction to Ergodic Theory, Princeton University Press, Princeton, 1976 |
| 17. |
M. B. Tabanov, “Separatrices splitting for Birkhoff's billiard in symmetric convex
domain, closed to an ellipse”, Chaos, 4:4 (1994), 595–606 |
| 18. |
M. Wojtkowski, “Principles for the design of billiards with nonvanishing Lyapunov
exponent”, Commun. Math. Phys., 105 (1986), 319–414 |
| 19. |
M. Wojtkowski, “Two applications of Jacobi fields to the billiard ball problem”, J. Differential Geom., 40:1 (1994), 155–164 |
