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On Escape rate for subshift with Markov measure
Published 10 Jan 2024 in math.DS | (2401.05118v2)
Abstract: In this paper, we consider a subshift of finite type with Markov measure. By considering a union of cylinders as holes, we investigate the exponential growth rate of measure of points whose orbits do not escape into the hole over a fixed number of iterations. We present two formulations for this escape rate: one based on the spectral radius of the Hadamard product of a related adjacency matrix and the stochastic matrix with respect to which the Markov measure is defined, and the other utilizing a recurrence relation. These formulations enable a comparative analysis of escape rates into distinct holes.
- Maximal escape rate for shifts. Discrete and Continuous Dynamical Systems, 42(12):6007–6029, 2022.
- Where to place a hole to achieve a maximal escape rate. Israel Journal of Mathematics, 182:229–252, 2011.
- Subshifts of finite type with a hole. J. Aust. Math. Soc., 115(1):73–98, 2023.
- The Yorke-Pianigiani measure and the asymptotic law on the limit Cantor set of expanding systems. Nonlinearity, 7(5):1437–1443, 1994.
- The Pianigiani-Yorke measure for topological Markov chains. Israel J. Math., 97:61–70, 1997.
- Mark F. Demers. Markov extensions and conditionally invariant measures for certain logistic maps with small holes. Ergodic Theory Dynam. Systems, 25(4):1139–1171, 2005.
- Limiting distributions for countable state topological Markov chains with holes. Discrete Contin. Dyn. Syst., 37(1):105–130, 2017.
- A separation theorem for nonsymmetric matrices. Journal of Mathematical Analysis and Applications, 23(1):209–212, 1968.
- C Haritha and Nikita Agarwal. Product of expansive Markov maps with hole. Discrete Contin. Dyn. Syst., 39(10):5743–5774, 2019.
- Eigenvalue interlacing for certain classes of matrices with real principal minors. Linear Algebra and its Applications, 88-89:373–403, 1987.
- N.J. Higham. Functions of Matrices: Theory and Computation. Other Titles in Applied Mathematics. SIAM, 2008.
- Expanding maps on sets which are almost invariant. Decay and chaos. Trans. Amer. Math. Soc., 252:351–366, 1979.
- N. N. Čencova. Statistical properties of smooth Smale horseshoes. In Mathematical problems of statistical mechanics and dynamics, volume 6 of Math. Appl. (Soviet Ser.), pages 199–256. Reidel, Dordrecht, 1986.
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