Limit cycles of planar polynomial vector fields
نویسندگان
چکیده
منابع مشابه
Lower Bounds for the Number of Orbital Topological Types of Planar Polynomial Vector Fields “modulo Limit Cycles”
We consider planar polynomial vector fields. We aim to find the (asymptotic) upper and lower bounds for the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert’s 16th problem. To circumvent this obstacle we introduce the notion of equivalence modulo limit cycles. Both upper and lower bounds can be obtained for ...
متن کاملUpper bounds for the number of orbital topological types of planar polynomial vector fields “ modulo limit cycles ”
The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert’s 16th problem. To circumvent this obstacle we introduce the notion of equivalence modulo limit cycles. This paper is the continuation of the author’s paper in [Mosc. Math. J. 1 (2001...
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One of the main problems in the qualitative theory of real planar differential systems is the determination of number and relative positions of limit cycles. The problem concerns “the most elusive” second part of Hilbert’s 16th problem (see [Smale, 1998; Lloyd, 1988]). In 1983, Jibin Li (see [Li, 2003; Li & Li, 1985; Li & Liu, 1991, 1992]) posed a method of detection functions to investigate po...
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One of the main problems in the qualitative theory of real planar differential systems is the determination of number and relative positions of limit cycles. The problem concerns “the most elusive” second part of Hilbert’s 16th problem (see [Smale, 1998; Lloyd, 1988]). In 1983, Jibin Li (see [Li, 2003; Li & Li, 1985; Li & Liu, 1991, 1992]) posed a method of detection functions to investigate po...
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In this article, a systematic procedure has been explored to studying general Zq-equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z12-equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2010
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.9648