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Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Deva\-ney-chaos and pos itive topological entropy seem to be the strongest. Let $A= \{0,1, \ldots, p-1\}$. We define a continuous map on $ A^{\mathbb Z}$ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points.
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참고문헌 (10)
참고문헌 신청
R. L. Adler / 1965 / Topological Entropy / Transactions of the American Mathematical Society 114(2):309
E. Akin / 1996 / When is a transitive map chaotic?, in Convergence in ergodic theory and probability (Columbus, OH, 1993), 25-40 / Ohio State Univ. Math. Res. Inst. Publ 5
N. Aoki / 1994 / Topological Theory of Dynamical Systems / North-Holland Publishing
E. M. Coven / 2006 / Every compact metric space that supports a positively expansive homeomorphism is nite, in Dynamics & Stochastics, vol. 48 of IMS Lecture Notes Monogr. Ser / Inst. Math. Statist 2006:304~305
S. Katok / 2007 / p-adic analysis compared with real / Amer-ican Mathematical Society
E. Akin / 1996 / When is a transitive map chaotic?, in Convergence in ergodic theory and probability (Columbus, OH, 1993), 25-40 / Ohio State Univ. Math. Res. Inst. Publ 5
N. Aoki / 1994 / Topological Theory of Dynamical Systems / North-Holland Publishing
E. M. Coven / 2006 / Every compact metric space that supports a positively expansive homeomorphism is nite, in Dynamics & Stochastics, vol. 48 of IMS Lecture Notes Monogr. Ser / Inst. Math. Statist 2006:304~305
S. Katok / 2007 / p-adic analysis compared with real / Amer-ican Mathematical Society
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