대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권4호
  • /
  • Pages.759-769
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  • 2006
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A CHARACTERIZATION OF HYPERBOLIC TORAL AUTOMORPHISMS

  • 발행 : 2006.10.31
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초록

Let L : $C\;\rightarrow\;C$ be a hyperbolic automorphism. Then the hyperbolic toral automorphism $L_A\;T^2\;\rightarrow\;T^2$, induced by L, is a chaotic map ([2] pg.192). We characterize hyperbolic toral automorphisms by proving the converse of the above statement.

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참고문헌

  1. J. Banks, J. Brooks, G. Cairns and P. Stacy, On Devany's definition of chaos, Amer. Math. Monthly 99 (1992), 332-334 https://doi.org/10.2307/2324899
  2. R. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Publ. Co., 1987
  3. S. Lattes, Sur l'iterationdes substitutions rationalles et les fonctions de Poincare, C. R. Acad. Sci. Paris 166 (1918), 26-28
  4. J. S. Lee, Regular branched covering spaces and chaotic maps on the Riemann sphere, Commun. Korean Math. Soc. 19 (2004), no. 3, 507-517 https://doi.org/10.4134/CKMS.2004.19.3.507
  5. P. Touhay, Yet another definition of chaos, Amer. Math. Monthly 104 (1997), 411-414 https://doi.org/10.2307/2974734