대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제34권3호
  • /
  • Pages.967-979
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  • 2019
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A DEVANEY-CHAOTIC MAP WITH POSITIVE ENTROPY ON A SYMBOLIC SPACE

  • 투고 : 2018.05.16
  • 심사 : 2018.08.29
  • 발행 : 2019.07.31
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초록

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 Devaney-chaos and pos itive topological entropy seem to be the strongest. Let $A=\{0,1,{\dots},p-1\}$. 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

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