Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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METRICAL AND TOPOLOGICAL PRESSURE OF FLOWS WITHOUT FIXED POINTS

  • Lianfa He (Department of Mathematics Hebei normal University) ;
  • Fenghong Yang (Department of Mathematics Sciences Tsinghua University) ;
  • Yinghui Gao (Academy of Mathematics and System Sciences Chinese Academy of Sciences)
  • Published : 2004.11.01
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Abstract

We study the metrical and topological pressure for flows without fixed points on a compact metric space, and get the results as follows: (1) The metrical pressure with respect to an ergodic measure can be defined by (t, $\varepsilon$)-spanning sets. (2) The topological pressure is the supremum of metrical pressures with respect to all ergodic measures. (3) The properties that the topological pressure is zero, nonzero, finite or infinite respectively are invariant under weak equivalence.

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References

  1. R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975), 181–202. https://doi.org/10.1007/BF01389848
  2. Lianfa He, Jinfeng Lv and Lina Zhou, Definition of measure-theoretic pressure using spanning sets, to appear in Acta Math. Sin. https://doi.org/10.1007/s10114-004-0368-5
  3. A. Katok, Lyapunov exponents, entropy and periodic points for diffeomorphisms, Publ. IHES. 51 (1980), 137–173. https://doi.org/10.1007/BF02684777
  4. R. Mane, Ergodic theory and differential dynamics, Springer, New-York. Berlin, 1987.
  5. M. E. Munroe, Introduction to measure and integration, Addison-wesley Publishing Company Inc. Cambridge, 42, MA. 1953.
  6. T. Ohno, A weak equivalence and topological entropy, Plub. Res. Inst. Math. Sci., Kyoto Univ. 16 (1980), 289–298. https://doi.org/10.2977/prims/1195187508
  7. Wenxiang Sun and Edson Varges, Entropy of flows, revisited, Bol. Soc. Brasil. Mat. 30 (1999), 315–333. https://doi.org/10.1007/BF01239009
  8. R. Thomas, Stability properties of one parameter flows, Proc. London Math. Soc. 45 (1982), 479–505. https://doi.org/10.1112/plms/s3-45.3.479
  9. P. Walters, An introduction to ergodic theory, Springer-Verlag, New-York, Heidelberg, Berlin, 1982.

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