A survey on local integrability and its regularity

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Cites Work

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First integrals of local analytic differential systems
Integrability of dynamical systems: algebra and analysis
Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
Generalized rational first integrals of analytic differential systems
Convergence versus integrability in Poincaré-Dulac normal form
First integrals and normal forms for germs of analytic vector fields
Local theory of nonlinear analytic ordinary differential equations
Convergence of Birkhoff normal forms for integrable systems
Local first integrals of differential systems and diffeomorphisms
Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance cases
On non-integrability of general systems of differential equations
Analytic integrable systems: analytic normalization and embedding flows
Smooth Gevrey normal forms of vector fields near a fixed point
Regularity and convergence of local first integrals of analytic differential systems
On the ultradifferentiable normalization
Convergence versus integrability in Birkhoff normal form
A note on local integrability of differential systems
Analytic normalization of analytically integrable differential systems near a periodic orbit
Analytic normalization of analytic integrable systems and the embedding flows
Local Darboux first integrals of analytic differential systems
On the nonexistence of rational first integrals for nonlinear systems and semiquasihomogeneous systems
Planar Dynamical Systems
Algebraic Particular Integrals, Integrability and the Problem of the Center
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

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