New lower bound for the number of critical periods for planar polynomial systems

2020/05/05 by Xiuli Cen, Cen, Xiuli
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Lipid metabolism and biosynthesis #math.DS

paper · pdf · doi:10.48550/arxiv.2005.02195

arxiv created 2020/05/05 · openalex publication_date 2020/05/05 · arxiv updated 2020/05/06 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct two classes of planar polynomial Hamiltonian systems having a center at the origin, and obtain the lower bounds for the number of critical periods for these systems. For polynomial potential systems of degree n, we provide a lower bound of n-2 for the number of critical periods, and for polynomial systems of degree n, we acquire a lower bound of n²/2+n-5/2 when n is odd and n²/2-2 when n is even for the number of critical periods. To the best of our knowledge, these lower bounds are new, moreover the latter one is twice the existing results up to the dominant term.

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