Subadditive pressure for ifs with triangular maps

• Autorzy: Barany B.
• Języki publikacji: EN

Abstrakty

EN

We investigate properties of the zero of the subadditive pressure which is a most important tool to estimate the Hausdorff dimension of the attractor of a non-conformal iterated function system (IFS) . Our result is a generalization of the main results of Miao and Falconer [Fractals 15 (2007)] and Manning and Simon [Nonlinearity 20 (2007)].

Słowa kluczowe

EN

Hausdorff dimension; contracting on average; subadditive pressure

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 3-4
• Strony: 263--278
• Opis fizyczny: Bibliogr. 11 poz., rys., wykr.

Twórcy

autor

Barany B.

• Department of Stochastics, Institute of Mathematics, Budapest University of Technics and Economics, P.O. Box 91, 1521 Budapest, Hungary,

Bibliografia

• [1] L. Barreira, A non-additive thermodynamic formalism and applications of dimension theory of hyperbolic dynamical systems, Ergodic Theory Dynam. Systems 16 (1996), 871-927.
• [2] K. Falconer, The Hausdorff dimension of self-affine fractals, Math. Proc. Cambridge Philos. Soc. 103 (1988), 339-350.
• [3] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, 1990.
• [4] K. Falconer, Bounded distortion and dimension for nonconformal repellers, Math. Proc. Cambridge Philos. Soc. 115 (1994), 315-334.
• [5] K. Falconer, Techniques in Fractal Geometry, Wiley, 1997.
• [6] K. Falconer and J. Miao, Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices, Fractals 15 (2007), 289-299.
• [7] U. Krengel, Ergodic Theory, de Gruyter, 1985.
• [8] A. Manning and K. Simon, Subadditive pressure for triangular maps, Nonlinearity 20 (2007), 133-149.
• [9] Ya. B. Pesin, Dimension Theory in Dynamical Systems, Univ. of Chicago Press, Chicago, 1997.
• [10] P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, New York, 1982.
• [11] Y. Zhang, Dynamical upper bounds for Hausdorff dimension of invariant sets, Ergodic Theory Dynam. Systems 17 (1997), 739-756.