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 Title: On the maximum number of limit cycles of certain polynomial Lienard equations Author(s): Yao, Leummim Doctoral Committee Chair(s): Albrecht, Felix Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: We consider the Lienard equation of the form$$\ddot x + \epsilon f(x)\dot x + x\sp{2m+1} = 0,\eqno(1)\cr$$which is equivalent to the planar system\eqalignno{\dot x &= y&\enspace\cr \dot{y} &= -x\sp{2m+1} - \epsilon f(x)y,&(2)\cr}where m is a nonnegative integer, f is a real polynomial and $\epsilon$ is a small parameter.We establish a sharp upper bound for the number of limit cycles (nontrivial isolated periodic orbits of system (2) depending on m and the degree of f provided $\epsilon$ is sufficiently small. This is done by investigating the fixed points of the Poincare return map associated with system (2).This result is an important step in the study of planar polynomial vector fields in connection with the second part of Hilbert's Sixteenth Problem, which is still an open question. Issue Date: 1995 Type: Text Language: English URI: http://hdl.handle.net/2142/22869 Rights Information: Copyright 1995 Yao, Leummim Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9624545 OCLC Identifier: (UMI)AAI9624545
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