Realization problems for limit cycles of planar polynomial vector fields
نویسندگان
چکیده
منابع مشابه
08w5055 Classical Problems on Planar Polynomial Vector Fields
At the end of the 19th century Poincaré and Hilbert stated three problems which are still open today: the problem of the center and the problem of Poincaré, stated by Poincaré in 1885 and in 1891, and Hilbert’s 16th problem, stated in Hilbert’s address at the International Congress of Mathematicians in Paris in 1900. The first two and the second part of Hilbert’s 16th problem are on planar poly...
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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 ...
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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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In this paper we give sufficient conditions to ensure uniqueness of limit cycles for a class of planar vector fields. We also exhibit a class of examples with exactly one limit cycle.
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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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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2016
ISSN: 0022-0396
DOI: 10.1016/j.jde.2015.10.044