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Statistical stability for multi-substitution tiling spaces

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  • Given a finite set $\{S_1\dots,S_k \}$ of substitution maps acting on a certain finite number (up to translations) of tiles in $\mathbb{R}^d$, we consider the multi-substitution tiling space associated to each sequence $\bar a\in \{1,\ldots,k\}^{\mathbb{N}}$. The action by translations on such spaces gives rise to uniquely ergodic dynamical systems. In this paper we investigate the rate of convergence for ergodic limits of patches frequencies and prove that these limits vary continuously with $\bar a$.
    Mathematics Subject Classification: Primary: 37A15, 37A25, 52C22.


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  • [1]

    F. Durand, Linearly recurrent subshifts have a finite number of non-periodic subshift factors, Ergodic Theory Dynamical Systems, 20 (2000), 1061-1078.doi: 10.1017/S0143385700000584.


    S. Ferenczi, Rank and symbolic complexity subshift factors, Ergodic Theory Dynamical Systems, 16 (1996), 663-682.doi: 10.1017/S0143385700009032.


    N. P. Frank, A primer of substitution tilings of the Euclidean plane, Expositiones Mathematicae, 26 (2008), 295-326.doi: 10.1016/j.exmath.2008.02.001.


    N. P. Frank and L. SadunFusion: A general framework for hierarchical tilings of $\mathbbR^d$, preprint, arXiv:1101.4930.


    F. Gähler and G. MaloneyCohomology of one-dimensional mixed substitution tiling spaces, preprint, arXiv:1112.1475.


    C. P. M. Geerse and A. Hof, Lattice gas models on self-similar aperiodic tilings, Rev. Math. Phys., 3 (1991), 163-221.doi: 10.1142/S0129055X91000072.


    W. H. Gottschalk, Orbit-closure decomposition and almost periodic properties, Bull. Amer. Math. Soc., 50 (1944), 915-919.doi: 10.1090/S0002-9904-1944-08262-1.


    Grünbaum and G. C. Shephard, "Tilings and Patterns," Freeman, New York, 1986.


    J.-Y. Lee, R. V. Moody and B. Solomyak, Pure point dynamical and diffraction spectra, Ann. Henri Poincaré, 3 (2002), 1003-1018.doi: 10.1007/s00023-002-8646-1.


    R. Pacheco and H. VilarinhoMetrics on tiling spaces, local isomorphism and an application of Brown's lemma, preprint, arXiv:1202.4902. doi: 10.1007/s00605-013-0484-3.


    C. Radin and M. Wolff, Space tilings and local isomorphism, Geometriae Dedicata, 42 (1992), 355-360.doi: 10.1007/BF02414073.


    E. A. Robinson, Jr., Symbolic dynamics and tilings of $\mathbbR^d$, Proc. Sympos. Appl. Math. Amer. Math. Soc., 60 (2004), 81-119.


    D. Ruelle, "Statistical Mechanics: Rigorous Results," W. A. Benjamin, Inc., New York - Amsterdam, 1969.


    B. Solomyak, Dynamics of self-similar tilings, Ergodic Theory and Dynamical Systems, 17 (1997), 695-738. Errata: Ergodic Theory and Dynamical Systems, 19 (1999), 1685.doi: 10.1017/S0143385797084988.

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