Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Rotating an interval and a circle
HTML articles powered by AMS MathViewer

by Alexander Blokh and Michał Misiurewicz PDF
Trans. Amer. Math. Soc. 351 (1999), 63-78 Request permission

Abstract:

We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the Black Sea.
References
  • Lluís Alsedà, Jaume Llibre, and MichałMisiurewicz, Combinatorial dynamics and entropy in dimension one, Advanced Series in Nonlinear Dynamics, vol. 5, World Scientific Publishing Co., Inc., River Edge, NJ, 1993. MR 1255515, DOI 10.1142/1980
  • A. M. Blokh, Rotation numbers, twists and a Sharkovskiĭ-Misiurewicz-type ordering for patterns on the interval, Ergodic Theory Dynam. Systems 15 (1995), no. 1, 1–14. MR 1314966, DOI 10.1017/S014338570000821X
  • A. Blokh and M. Misiurewicz, Entropy of twist interval maps, Isr. J. Math. 102 (1997), 61–99.
  • —, New order for periodic orbits of interval maps, Ergod. Th. & Dynam. Sys. 17 (1997), 565–574.
  • —, Entropy and over-rotation numbers for interval maps, Proc. Steklov Inst. Math. 216 (1997), 229–235.
  • J. Bobok and M. Kuchta, X-minimal patterns and a generalization of Sharkovskii’s theorem, Fund. Math. 156 (1998), 33-66.
  • MichałMisiurewicz and Zbigniew Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 94 (1991), no. 456, vi+112. MR 1086562, DOI 10.1090/memo/0456
  • S. Newhouse, J. Palis, and F. Takens, Bifurcations and stability of families of diffeomorphisms, Inst. Hautes Études Sci. Publ. Math. 57 (1983), 5–71. MR 699057, DOI 10.1007/BF02698773
  • H. Poincaré, Sur les courbes définies par les équations différentielles, Oeuvres completes, vol. 1, 137–158, Gauthier-Villars, Paris, 1952.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 54H20, 58F03, 58F08
  • Retrieve articles in all journals with MSC (1991): 54H20, 58F03, 58F08
Additional Information
  • Alexander Blokh
  • Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
  • MR Author ID: 196866
  • Email: ablokh@math.uab.edu
  • Michał Misiurewicz
  • Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
  • MR Author ID: 125475
  • Email: mmisiure@math.iupui.edu
  • Received by editor(s): August 26, 1996
  • Additional Notes: The first author was partially supported by the NSF grant DMS-9626303. The second author was partially supported by the NSF grant DMS-9305899
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 63-78
  • MSC (1991): Primary 54H20, 58F03, 58F08
  • DOI: https://doi.org/10.1090/S0002-9947-99-02367-3
  • MathSciNet review: 1621717