A note on local integrability of differential systems

DOI10.1016/j.jde.2017.08.016zbMath1385.34004arXiv1712.09510OpenAlexW2750196302MaRDI QIDQ2407129

Xiang Zhang

Publication date: 28 September 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09510

zbMATH Keywords

invariant manifoldanalytic differential systemslocal integrabilitynon-isolated singular point

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Explicit solutions, first integrals of ordinary differential equations (34A05) Invariant manifolds for ordinary differential equations (34C45)

Related Items (6)

A survey on local integrability and its regularity ⋮ Analytically integrable system orbitally equivalent to a semi-quasihomogeneous system ⋮ On the local Gevrey integrability ⋮ Analytic integrability around a nilpotent singularity ⋮ Rational Integrability of the Maxwell–Bloch System ⋮ Regularity and convergence of local first integrals of analytic differential systems

Cites Work

• First integrals of local analytic differential systems
• Generalized rational first integrals of analytic differential systems
• Convergence versus integrability in Poincaré-Dulac normal form
• Varieties of local integrability of analytic differential systems and their applications
• First integrals and normal forms for germs of analytic vector fields
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Geometric singular perturbation theory for ordinary differential equations
• Convergence of Birkhoff normal forms for integrable systems
• Local first integrals of differential systems and diffeomorphisms
• On non-integrability of general systems of differential equations
• Analytic integrable systems: analytic normalization and embedding flows
• Convergence versus integrability in Birkhoff normal form
• Analytic normalization of analytic integrable systems and the embedding flows
• On the nonexistence of rational first integrals for nonlinear systems and semiquasihomogeneous systems
• The Center and Cyclicity Problems
• Birkhoff normalization and superintegrability of Hamiltonian systems
• Non-integrability for general nonlinear systems
• Varieties and analytic normalizations of partially integrable systems
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A note on local integrability of differential systems