2011/09/21 by A. Raouf Chouikha, Chouikha, A. Raouf · 1 citation
Mathematics · Physics and Astronomy · #34C05 #34C25 #34C35 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.DS #math.MP #msc:34C05 #msc:34C25 #msc:34C35
paper · pdf · doi:10.48550/arxiv.1109.4611
30 pages
openalex publication_date 2011/09/21 · arxiv created 2011/11/03 · arxiv updated 2011/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are interested at first in the study of the monotonicity for the period function of the conservative equation (1) x + g(x) = 0. Some refinements of known criteria are brought. Moreover, we give necessary and sufficient conditions so that the analytic potential of equation (1) is isochronous. These conditions which are different from those introduced firstly by Koukles and Piskounov and thereafter by Urabe appear sometime to be easier to use. We then apply these results to produce families of isochronous potentials depending on many parameters, some of them are news. Moreover, analytic isochronicity requirements of parametrized potentials will also be considered