On the period function of Newtonian systems

2013/02/26 by A. Raouf Chouikha, Chouikha, A. Raouf, Mohsen Timoumi +1
Mathematics · Physics and Astronomy · #34C15 #34C23 #34C25 #34C37 #37G15 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.DS #math.MP #msc:34C15 #msc:34C23 #msc:34C25 #msc:34C37 #msc:37G15

paper · pdf · doi:10.48550/arxiv.1302.6400

16 pages

arxiv created 2013/02/26 · arxiv updated 2013/02/27

Abstract

We study the existence of centers of planar autonomous system of the form (S) x=y, y = -h(x) - g(x)y - f(x)y². We are interested in the period function T around a center 0. A sufficient condition for the isochronicity of (S) at 0 is given. Such a condition is also necessary when f,g,h are analytic functions. In that case a characterization of isochronous centers of system (S) is given. Some applications will be derived. In particular, new families of isochronous centers will be described

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