RESEARCH ARTICLE

Quadratic perturbations of a quadratic reversible center of genus one

  • Linping PENG
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  • School of Mathematics and System Sciences, Beijing University of Aeronautics and Astronautics, LIMB of the Ministry of Education, Beijing 100191, China

Received date: 25 Jan 2010

Accepted date: 27 Jul 2011

Published date: 01 Oct 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

In this paper, we study a reversible and non-Hamitonian system with a period annulus bounded by a hemicycle in the Poincaré disk. It is proved that the cyclicity of the period annulus under quadratic perturbations is equal to two. This verifies some results of the conjecture given by Gautier et al.

Cite this article

Linping PENG . Quadratic perturbations of a quadratic reversible center of genus one[J]. Frontiers of Mathematics in China, 2011 , 6(5) : 911 -930 . DOI: 10.1007/s11464-011-0155-4

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