Local inverses of shift maps along orbits of flows

Details Local inverses of shift maps along orbits of flows Local inverses of shift maps along orbits of flows

2008-06-09

arxiv.org/abs/0806.1502v3

Mathematics

Dynamical Systems

43 pages, 4 figures. V3. The class of admissible singularities for vector field is extended

Scientific paper

Let M be a smooth manifold and F be a vector field on $M$. My article ["Smooth shifts along trajectories of flows", Topol. Appl. 130 (2003) 183-204, arXiv:math/0106199] concerning the homotopy types of the group of diffeomorphisms preserving orbits of F contains two errors. They imply that the principal statement of that paper holds under additional assumptions on F. Unfortunately this result was essentially used in another paper of mine ["Homotopy types of stabilizers and orbits of Morse functions on surfaces" Ann. Glob. Anal. Geom., 29 no. 3, (2006) 241-285, arXiv:math/0310067]. The aim of this article is to expose the results of the first paper in a right way, extend them to a larger class of flows with degenerate singularities, and show that the results of the second paper remain true.

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