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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
[2]
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
Chernov, N. and Markarian, R., Chaotic Billiards, Mathematical Surveys and Monographs, 127 (American Mathematical Society, Providence, RI, 2006).CrossRefGoogle Scholar
[5]
Ikawa, M., ‘Decay of solutions of the wave equation in the exterior of several convex bodies’, Ann. Inst. Fourier38(2) (1988), 113–146.CrossRefGoogle Scholar
[6]
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
[7]
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
[8]
Pesin, Y., Dimension Theory in Dynamical Systems: Contemporary Views and Applications, Chicago Lectures in Mathematics (University of Chicago Press, 1997).CrossRefGoogle Scholar
[9]
Ruelle, D., ‘Differentiation of SRB states’, Comm. Math. Phys.187(1) (1997), 227–241.CrossRefGoogle Scholar
[10]
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
[11]
Stoyanov, L., ‘Non-integrability of open billiard flows and Dolgopyat-type estimates’, Ergod. Th. & Dynam. Sys.32(1) (2011), 295–313.CrossRefGoogle Scholar
[12]
Varah, J., ‘A lower bound for the smallest singular value of a matrix’, Linear Algebra Appl.11(1) (1975), 3–5.CrossRefGoogle Scholar
[13]
Wright, P., ‘Estimates of Hausdorff dimension for non-wandering sets of higher dimensional open billiards’, Canad. J. Math.65 (2013), 1384–1400.CrossRefGoogle Scholar
[14]
Wright, P., ‘Differentiability of Hausdorff dimension of the non-wandering set in a planar open billiard’, Preprint, 2014, arXiv:1401.1002v3.Google Scholar
[15]
Wright, P., ‘Hausdorff dimension of non-wandering sets for average conformal hyperbolic maps’, Preprint, 2014, arXiv:1401.1005v2.Google Scholar