Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-26T02:21:27.464Z Has data issue: false hasContentIssue false

DIMENSIONAL CHARACTERISTICS OF THE NONWANDERING SETS OF OPEN BILLIARDS

Published online by Cambridge University Press:  11 August 2015

PAUL WRIGHT*
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia email paul@madgech.com
Rights & Permissions [Opens in a new window]

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Abstracts of Australasian PhD Theses
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Ban, J., Cao, Y. and Hu, H., ‘The dimensions of a non-conformal repeller and an average conformal repeller’, Trans. Amer. Math. Soc. 362(2) (2010), 727751.CrossRefGoogle Scholar
Barreira, L., ‘A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems’, Ergod. Th. & Dynam. Sys. 16(5) (1996), 871927.CrossRefGoogle Scholar
Barreira, L., ‘Dimension estimates in nonconformal hyperbolic dynamics’, Nonlinearity 16(5) (2003), 16571672.CrossRefGoogle Scholar
Chernov, N. and Markarian, R., Chaotic Billiards, Mathematical Surveys and Monographs, 127 (American Mathematical Society, Providence, RI, 2006).CrossRefGoogle Scholar
Ikawa, M., ‘Decay of solutions of the wave equation in the exterior of several convex bodies’, Ann. Inst. Fourier 38(2) (1988), 113146.CrossRefGoogle Scholar
Katok, A., Knieper, G., Pollicott, M. and Weiss, H., ‘Differentiability and analyticity of topological entropy for Anosov and geodesic flows’, Invent. Math. 98(3) (1989), 581597.CrossRefGoogle Scholar
Kenny, R., ‘Estimates of Hausdorff dimension for the non-wandering set of an open planar billiard’, Canad. J. Math. 56(1) (2004), 115133.CrossRefGoogle Scholar
Pesin, Y., Dimension Theory in Dynamical Systems: Contemporary Views and Applications, Chicago Lectures in Mathematics (University of Chicago Press, 1997).CrossRefGoogle Scholar
Ruelle, D., ‘Differentiation of SRB states’, Comm. Math. Phys. 187(1) (1997), 227241.CrossRefGoogle Scholar
Stoyanov, L., ‘An estimate from above of the number of periodic orbits for semi-dispersed billiards’, Comm. Math. Phys. 124(2) (1989), 217227.CrossRefGoogle Scholar
Stoyanov, L., ‘Non-integrability of open billiard flows and Dolgopyat-type estimates’, Ergod. Th. & Dynam. Sys. 32(1) (2011), 295313.CrossRefGoogle Scholar
Varah, J., ‘A lower bound for the smallest singular value of a matrix’, Linear Algebra Appl. 11(1) (1975), 35.CrossRefGoogle Scholar
Wright, P., ‘Estimates of Hausdorff dimension for non-wandering sets of higher dimensional open billiards’, Canad. J. Math. 65 (2013), 13841400.CrossRefGoogle Scholar
Wright, P., ‘Differentiability of Hausdorff dimension of the non-wandering set in a planar open billiard’, Preprint, 2014, arXiv:1401.1002v3.Google Scholar
Wright, P., ‘Hausdorff dimension of non-wandering sets for average conformal hyperbolic maps’, Preprint, 2014, arXiv:1401.1005v2.Google Scholar