DOI: 10.1007/bf01205934. Principles for the design of billiards with nonvanishing Lyapunov exponents

Principles for the design of billiards with nonvanishing Lyapunov exponents

10.1007/bf01205934

Crossref journal-article

Springer Science and Business Media LLC

Communications in Mathematical Physics (297)

Authors 1

Maciej Wojtkowski (first)

References 18 Referenced 170

Arnold, V.I.: Mathematical methods of classical mechanics. Berlin, Heidelberg, New York: Springer 1978 (10.1007/978-1-4757-1693-1) / Mathematical methods of classical mechanics by V.I. Arnold (1978)
Benettin, G.: Power law behavior of Lyapunov exponents in some conservative dynamical systems. Physica13 D, 211?220 (1984) / Physica by G. Benettin (1984)
Benettin, G., Strelcyn, J.-M.: Numerical experiments on the free motion of a point mass moving in a plane convex region: stochastic transition and entropy. Phys. Rev. A17, 773?785 (1978) (10.1103/PhysRevA.17.773) / Phys. Rev. by G. Benettin (1978)
Birkhoff, G.: Lattice theory, AMS Colloquium Publications, Vol. 25, 3rd Ed. Chap. XVI (1968)
Bunimovich, L.A.: On the ergodic properties of nowhere dispersing billiards. Commun. Math. Phys.65, 295?312 (1979) (10.1007/BF01197884) / Commun. Math. Phys. by L.A. Bunimovich (1979)
Bunimovich, L.A., Sinai, Ya.G.: On a fundamental theorem in the theory of dispersing billiards. Math. USSR, Sb.19, 3, 407?423 (1973) (10.1070/SM1973v019n03ABEH001786) / Math. USSR, Sb. by L.A. Bunimovich (1973)
Cornfeld, I.P., Fomin, S.V., Sinai, Ya.G.: Ergodic theory. Berlin, Heidelberg, New York: Springer 1982, Chap. 6 (10.1007/978-1-4615-6927-5) / Ergodic theory by I.P. Cornfeld (1982)
Douady, R.: Applications du théorème des tores invariants. Thesis, University of Paris VII (1982)
Katok, A., Strelcyn, J.-M. In collaboration with Ledrappier, F., Przytycki, F.: Smooth maps with singularities: Invariant manifolds entropy and billiards. Lecture Notes in Mathematics (to appear)
Lazutkin, V.F.: On the existence of caustics for the billiard ball problem in a convex domain. Math. USSR, Izv.7, 185?215 (1973) (10.1070/IM1973v007n01ABEH001932) / Math. USSR, Izv. by V.F. Lazutkin (1973)
Ledrappier, F., Strelcyn, J.-M.: A proof of the estimation from below in Pesin's entropy formula. Ergodic Theory Dyn. Syst.2, 203?219 (1982) (10.1017/S0143385700001528) / Ergodic Theory Dyn. Syst. by F. Ledrappier (1982)
Mather, J.N.: Glancing billiards. Ergodic Theory Dyn. Syst.2, 397?403 (1982) (10.1017/S0143385700001681) / Ergodic Theory Dyn. Syst. by J.N. Mather (1982)
Oseledec, V.I.: The multiplicative ergodic theorem. The Lyapunov characteristic numbers of a dynamical system. Trans. Mosc. Math. Soc.19, 197?231 (1968) / Trans. Mosc. Math. Soc. by V.I. Oseledec (1968)
Pesin, Ya. B.: Lyapunov characteristic exponents and smooth ergodic theory. Russ. Math. Surveys32, 4, 55?114 (1977) (10.1070/RM1977v032n04ABEH001639) / Russ. Math. Surveys by Ya. B. Pesin (1977)
Robnik, M.: Classical dynamics of a family of billiards with analytic boundaries. J. Phys. A: Math. Gen.16, 3971?3986 (1983) (10.1088/0305-4470/16/17/014) / J. Phys. A: Math. Gen. by M. Robnik (1983)
Sinai, Ya. G.: Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards. Russ. Math. Surveys25, 2, 137?189 (1970) (10.1070/RM1970v025n02ABEH003794) / Russ. Math. Surveys by Ya. G. Sinai (1970)
Wojtkowski, M.: Invariant families of cones and Lyapunov exponents. Ergodic Theory Dyn. Syst.5, 145?161 (1985) (10.1017/S0143385700002807) / Ergodic Theory Dyn. Syst. by M. Wojtkowski (1985)
Wojtkowski, M.: On uniform contraction generated by positive matrices. In: Random matrices and their applications. Cohen, J.E., Kesten, H., Newman, C.M. (eds.). Contemporary Mathematics Vol. 50. AMS 1986 (10.1090/conm/050/841086)

Dates

Type	When
Created	20 years, 6 months ago (Feb. 25, 2005, 10:33 a.m.)
Deposited	6 years, 3 months ago (May 1, 2019, 1:06 p.m.)
Indexed	4 weeks ago (Aug. 2, 2025, 1:13 a.m.)
Issued	38 years, 11 months ago (Sept. 1, 1986)
Published	38 years, 11 months ago (Sept. 1, 1986)
Published Print	38 years, 11 months ago (Sept. 1, 1986)

Funders 0

None

BibTeX

@article{Wojtkowski_1986, title={Principles for the design of billiards with nonvanishing Lyapunov exponents}, volume={105}, ISSN={1432-0916}, url={http://dx.doi.org/10.1007/bf01205934}, DOI={10.1007/bf01205934}, number={3}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Wojtkowski, Maciej}, year={1986}, month=sep, pages={391–414} }

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