Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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.

 

Dynamical systems with cross-sections
HTML articles powered by AMS MathViewer

by Dean A. Neumann PDF
Proc. Amer. Math. Soc. 56 (1976), 339-344 Request permission

Abstract:

The problem of classifying dynamical systems (flows) with global cross-sections in terms of the associated diffeomorphisms of the cross-sections is considered. Suppose that, for $i = 1,2,{\phi _i}$ is a ${C^r}$ flow $(r \geqslant 0)$ on the ${C^r}$ manifold ${M_i}$ that admits a global cross-section ${S_i} \subseteq {M_i}$ with associated diffeomorphism (’first return map’) ${d_i}$. If rank $({H_1}({M_1};{\mathbf {Z}})) = 1$, then $({M_1},{\phi _1})$ is ${C^s}$ equivalent $(s \leqslant r)$ to $({M_2},{\phi _2})$ if and only if ${d_1}$ is ${C^s}$ conjugate to ${d_2}$. If rank $({H_1}({M_1};{\mathbf {Z}})) \ne 1$ and ${\phi _1}$ has a periodic orbit, then there are infinitely many global cross-sections ${T_i} \subseteq {M_1}$ of ${\phi _1}$, such that the associated diffeomorphisms are pairwise nonconjugate.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F99, 57D50
  • Retrieve articles in all journals with MSC: 58F99, 57D50
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 339-344
  • MSC: Primary 58F99; Secondary 57D50
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0407903-9
  • MathSciNet review: 0407903