3/22/2023 0 Comments Clemens subshift universal![]() ![]() 1930) and in its variants which all admit a natural formulation in terms of properties satisfied by badly approximable vectors. In this respect, they play a crucial role in many problems well beyond Number Theory and Fractal Geometry (e.g., in signal processing, in mathematical physics and in convex geometry).Īfter outlining some of the latest developments in this very active area of research, we will take an interest in the Littlewood conjecture (c. This is joint work with Stefano Marmi.įaustin Adiceam (Université Paris-Est Créteil): Badly approximable vectors and Littlewood-type problems ( paper)īadly approximable vectors are fractal sets enjoying rich Diophantine properties. Then we discuss the L p and the Hölder regularity properties of the difference between the classical Brjuno function and the Brjuno-type functions. In this talk, we introduce Brjuno-type functions associated with by-excess, odd and even continued fractions with a number theoretical motivation. Yoccoz introduced the Brjuno function which characterizes the Brjuno numbers to estimate the size of Siegel disks. The importance of Brjuno numbers comes from the study of one variable analytic small divisor problems. Seul Bee Lee (Institute for Basic Science): Regularity properties of Brjuno functions associated with by-excess, odd and even continued fractions ( paper)Īn irrational number is called a Brjuno number if the sum of the series of log(q n+1)/q n converges, where q n is the denominator of the n-th principal convergent of the regular continued fraction. This talk is based on joint work with Y.-J. Similar questions are also discussed for 0-1 apwenian sequences. Moreover, the number of ☑ apwenian sequences is given explicitly. This allows us to discuss the Diophantine property of the values of their generating functions at 1/b where b ≥ 2 is an integer. In particular, the Hankel determinants of apwenian sequences do not vanish. The Hankel determinants of these ☑ sequences share the same property as the Hankel determinants of the Thue-Morse sequence found by Allouche, Peyrière, Wen and Wen in 1998. In this talk, we will introduce a class of ☑ sequences, called the apwenian sequences. Wen Wu (South China University of Technology): From the Thue-Morse sequence to the apwenian sequences ( slides) ( journal) ( arXiv) If you want to participate in the seminar, please contact the organisers ( Shigeki Akiyama, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner) by email to 8, 2022, 14:00 CET (UTC +1) Jr.: Theory of Recursive Functions and Effective Computability.This is an online seminar on numeration systems and related topics (see the series of Numeration conferences), in the spirit of other One World Seminars talks are on Zoom. Robinson, R.M.: Undecidability and nonperiodicity for tilings of the plane. Pavlov, R., Schraudner, M.: Classification of sofic projective subdynamics of multidimensional shifts of finite type (2010, submitted) Mozes, S.: Tilings, substitution systems and dynamical systems generated by them. Cambridge University Press, Cambridge (1995) Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Hochman, M.: On the dynamics and recursive properties of multidimensional symbolic systems. Hedlund, G.A.: Endomorphisms and automorphisms of the shift dynamical system. ![]() Hanf, W.: Nonrecursive tilings of the plane. I. 276–288 (2008)ĭurand, B., Romashchenko, A.E., Shen, A.: Fixed-point tile sets and their applications (2010). ACM, New York (2001)ĭurand, B., Romashchenko, A.E., Shen, A.: Fixed point and aperiodic tilings. ![]() In: STOC’01: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, pp. Soc., Providence (1966)īoyle, M.: Open problems in symbolic dynamics. Masson, Paris (1993)īerger, R.: The Undecidability of the Domino Problem. In: 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009), vol. ![]() Aubrun, N., Sablik, M.: An order on sets of tilings corresponding to an order on languages. ![]()
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