A numerical view on topological transitivity and mixing for symbolic dynamics

• Autorzy: Jabłoński D. , Oprocha P.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to give some algorithms detecting topological transitivity, mixing and other properties of subshifts of finite type.

Słowa kluczowe

EN

subshift finite type; topological transitivity; topological mixing; algorithms; symbolic dynamics

PL

przesunięcie skończonego rodzaju; przechodniość topologiczna; algorytmy; dynamika symboliczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 1
• Strony: 229--238
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Jabłoński D.

autor

Oprocha P.

• Institute of Mathematics Cracow University of Technology Kraków, Poland,

Bibliografia

• [1] T. H. Cormen, C. E. Leiserson and R. L. Rivest, Introduction to Algorithms, Cambridge, 1991.
• [2] R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, New York, 1989.
• [3] Z. Galias, P. Zgliczyński, Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Henon map, Nonlinearity 14 (2001), no. 5, 909–932.
• [4] D. Jabłoński, Numerical conditions for some dynamical properties of subshifts of finite type, Demonstratio Math. 34 (2001), no. 4, 969–974.
• [5] D. Jabłoński, Dynamical properties of finite type subshifts generated by a sum of (0, 1)-square matrices, Demonstratio Math. 35 (2002), no. 4, 891–897.
• [6] D. Jabłoński, M. Kulczycki, Topological transitivity, mixing and nonwandering set of subshifts of finite type-a numerical approach, Int. J. Comput. Math. 80 (2003), no. 6, 671–677.
• [7] D. Lind, B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995.
• [8] R. Mane, Ergodic Theory and Differentiable Dynamics, Springer Verlag, Berlin, 1987.