ENTROPY, POSITIVELY CONTINUUM-WISE EXPANSIVENESS AND SHADOWING

DOI QR코드

DOI QR Code

Lee, Manseob;Park, Junmi

  • 투고 : 2015.10.15
  • 심사 : 2015.11.05
  • 발행 : 2015.11.15

초록

Let (X, d) be a compact metric space, and let $f:X{\rightarrow}X$ be a continuous map. We consider that if a positively continuum-wise expansiveness continuous map f has the positively shadowing property in the nonwandering set, then the topological entropy is positive.

키워드

positively continuum-wise expansive;positively measure expansive;entropy;shadowing

참고문헌

  1. A. Artigue and D. Carrasco-Olivera, A note on measure-expansive di eomor- phisms, J. Math. Anal. Appl. 428 (2015), 713-716. https://doi.org/10.1016/j.jmaa.2015.02.052
  2. H. Kato, Continuum-wise expansive homeomorphisms, Canad. J. Math. 45 (1993), 576-598. https://doi.org/10.4153/CJM-1993-030-4
  3. C. A. Morales, Entropy, pseudo-orbit tracing property and positively expansive measure, preprint, arxiV:1409.3470v1.
  4. T. K. S. Moothathu, Implications of pseudo-orbit tracing property for continu- ous maps on compacta, Topol. Appl, 158 (2011), 2232-2239. https://doi.org/10.1016/j.topol.2011.07.016

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)