Complex planar Hamiltonian systems: linearization and dynamics
type: Item
instance of: scholarly article
title: Complex planar Hamiltonian systems: linearization and dynamics
zbMATH Open document ID: 1478.37061
author: Yanyan Li
published in: Discrete and Continuous Dynamical Systems
publication date: 2021-06-08T00:00:00Z
review text: By now, there are lots of known results on real planar Hamiltonian systems but very few known results on complex planar Hamiltonian systems. The study of the dynamics of complex planar Hamiltonian systems has not only its own theoretical importance but also many practical applications. This work focuses on the global dynamics of complex planar Hamiltonian polynomial systems. Firstly, for general complex quadratic Hamiltonian systems of one degree of freedom, the authors give some sufficient conditions on the existence of family of invariant tori. Secondly, they complete the characterization of locally analytic linearizability of complex planar Hamiltonian systems with homogeneous nonlinearity of degrees either 2 or 3 at a nondegenerate singularity. Their global dynamics is investigated. Finally, for these classes of systems, they prove the existence of families of invariant tori, together with isochronous periodic orbits.
reviewed by: Jie Liu
Mathematics Subject Classification ID: 37J38
Mathematics Subject Classification ID: 37J46
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 7356238
zbMATH Keywords: complex Hamiltonian system
zbMATH Keywords: Liouvillian integrability
zbMATH Keywords: linearization
zbMATH Keywords: global dynamics
zbMATH Keywords: invariant tori
MaRDI profile type: Publication
full work available at URL: dcds.2020406
OpenAlex ID: W3112971671
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DOI: 10.3934/DCDS.2020406
description: scientific article; zbMATH DE number 7356238