Normalizers of planar systems with known first integrals
Marco Sabatini
TL;DR
This paper presents methods to find normalizers for planar differential systems with known first integrals and provides an integral formula for the period function derivative in systems with a center.
Contribution
It introduces a systematic approach to find normalizers in planar systems with first integrals and derives a new integral formula for the period function derivative in systems with centers.
Findings
Method to find normalizers for systems with known first integrals
Integral formula for the derivative of the period function in systems with centers
Enhanced understanding of the structure of planar systems with first integrals
Abstract
Given a planar differential system with a first integral, we show how to find a normalizer. For systems with a center, we give an integral formula for the derivative of its period function.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Control and Dynamics of Mobile Robots · Advanced Differential Geometry Research