Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Gutkin, Billiards on almost integrable polyhedral surfaces, Erg. Th. and Dyn. Syst., 4, N4(1984), 569–584.
P. R. Halmos, Lectures on Ergodic Theory, Tokyo, 1956.
A. Katok, Constructions in Ergodic Theory, Part 1, preprint, to appear in Birkhauser, Progress in Math.
A. Katok, Ergodicity of generic irrational billiards, Abstracts from workshop on 2-manifolds and Geometry, Oct. 1984, MSRI, Jan. 1986.
A. Katok, The growth rate for the number of singular and periodic orbits for a polygonal billiard, preprint, 1984.
A. Katok, Interval exchange transformations and some special flows are not mixing, Israel J. of Math. 35 (1980), 301–310.
S. Kerckhoff, H. Masur, J. Smillie, Ergodicity of billiard lows and quadratic differentials, to appear in Ann. of Math.
E. A. Sataev, On the number of invariant measures for flows on orientable surfaces, Math. of the USSR, Izrestija 9(1975), 813–830.
P. Walters, An introduction to ergodic theory, Springer-Verlag, 1982.
A Zemlyakov, A. Katok, Topological transitivity of billiards in polygons, Math. Notes of the USSR Acad. Sci. 18 N2(1975), 760–764.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Gutkin, E., Katok, A. (1988). Weakly mixing billiards. In: Gomez-Mont, X., Seade, J.A., Verjovski, A. (eds) Holomorphic Dynamics. Lecture Notes in Mathematics, vol 1345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081401
Download citation
DOI: https://doi.org/10.1007/BFb0081401
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50226-5
Online ISBN: 978-3-540-45957-6
eBook Packages: Springer Book Archive