Fixed points of the area preserving Poincaré maps on two-manifolds
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Abstract:
We study the number of fixed points of the area preserving Poincaré map $P$ associated to periodic in time ODE’s on two-manifolds. We prove the fixed point index formula for the Poincaré map based on the method of periodic isolating segments. As the application we show that the $1$-periodic hamiltonian planar system \[ \dot {z}=\overline {z}^n+e^{2\pi i t}\overline {z}^l \] has at least $n+1$ non-zero $1$-periodic solutions provided that $l>n\geq 1$.References
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Additional Information
- Klaudiusz Wójcik
- Affiliation: Department of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
- Email: Klaudiusz.Wojcik@uj.edu.pl
- Received by editor(s): October 9, 2015
- Received by editor(s) in revised form: December 29, 2016
- Published electronically: June 16, 2017
- Communicated by: Yingfei Yi
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5223-5233
- MSC (2010): Primary 34C25; Secondary 37B30
- DOI: https://doi.org/10.1090/proc/13642
- MathSciNet review: 3717951