On the upper bound of the criticality of potential systems at the outer\n boundary using the Roussarie-Ecalle compensator

2017/12/23 by David Rojas, Rojas, David
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1712.08756

openalex publication_date 2017/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

This paper is concerned with the study of the criticality of families of\nplanar centers. More precisely, we study sufficient conditions to bound the\nnumber of critical periodic orbits that bifurcate from the outer boundary of\nthe period annulus of potential centers. In the recent years, the new approach\nof embedding the derivative of the period function into a collection of\nfunctions that form a Chebyshev system near the outer boundary has shown to be\nfruitful in this issue. In this work, we tackle with a remaining case that was\nnot taken into account in the previous studies in which the Roussarie-Ecalle\ncompensator plays an essential role. The theoretical results we develop are\napplied to study the bifurcation diagram of the period function of two\ndifferent families of centers: the power-like family x=x^p-x^q,\np,q\∈\ℝ with p>q; and the family of dehomogenized Loud's centers.\n

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