Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Fixed points of the area preserving Poincaré maps on two-manifolds


Author: Klaudiusz Wójcik
Journal: Proc. Amer. Math. Soc. 145 (2017), 5223-5233
MSC (2010): Primary 34C25; Secondary 37B30
DOI: https://doi.org/10.1090/proc/13642
Published electronically: June 16, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

$\displaystyle \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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 34C25, 37B30

Retrieve articles in all journals with MSC (2010): 34C25, 37B30


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

DOI: https://doi.org/10.1090/proc/13642
Keywords: Lefschetz number, isolating blocks, periodic segments, fixed point index, planar hamiltonian systems, Poincar\'e map
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
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society