No CrossRef data available.
Article contents
DIMENSIONAL CHARACTERISTICS OF THE NONWANDERING SETS OF OPEN BILLIARDS
Published online by Cambridge University Press: 11 August 2015
Abstract
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
- Type
- Abstracts of Australasian PhD Theses
- Information
- Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 511 - 513
- 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), 727–751.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), 871–927.CrossRefGoogle Scholar
Barreira, L., ‘Dimension estimates in nonconformal hyperbolic dynamics’, Nonlinearity 16(5) (2003), 1657–1672.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), 113–146.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), 581–597.CrossRefGoogle Scholar
Kenny, R., ‘Estimates of Hausdorff dimension for the non-wandering set of an open planar billiard’, Canad. J. Math. 56(1) (2004), 115–133.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), 227–241.CrossRefGoogle Scholar
Stoyanov, L., ‘An estimate from above of the number of periodic orbits for semi-dispersed billiards’, Comm. Math. Phys. 124(2) (1989), 217–227.CrossRefGoogle Scholar
Stoyanov, L., ‘Non-integrability of open billiard flows and Dolgopyat-type estimates’, Ergod. Th. & Dynam. Sys. 32(1) (2011), 295–313.CrossRefGoogle Scholar
Varah, J., ‘A lower bound for the smallest singular value of a matrix’, Linear Algebra Appl. 11(1) (1975), 3–5.CrossRefGoogle Scholar
Wright, P., ‘Estimates of Hausdorff dimension for non-wandering sets of higher dimensional open billiards’, Canad. J. Math. 65 (2013), 1384–1400.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
You have
Access