First integrals of local analytic differential systems

DOI10.1016/j.bulsci.2011.10.003zbMath1245.34004OpenAlexW2010999652MaRDI QIDQ414802

Sebastian Walcher, Chara Pantazi, Jaume Llibre

Publication date: 11 May 2012

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2011.10.003

zbMATH Keywords

centerNormal formreversible systemformal first integrals

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) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05) Invariant manifolds for ordinary differential equations (34C45) Ordinary differential equations on complex manifolds (34M45)

Related Items (25)

Local Darboux first integrals of analytic differential systems ⋮ Zero-Hopf polynomial centers of third-order differential equations ⋮ A note on local integrability of differential systems ⋮ Local integrability and linearizability of a \((1:-1:-1)\) resonant quadratic system ⋮ The three-dimensional center problem for the zero-Hopf singularity ⋮ The center problem for a \({1:-4}\) resonant quadratic system ⋮ Time-Reversibility and Ivariants of Some 3-dim Systems ⋮ A survey on local integrability and its regularity ⋮ Complete integrability and time-reversibility of some 3-dim systems ⋮ Integrability and linearizability of symmetric three-dimensional quadratic systems ⋮ Invariant algebraic surfaces of polynomial vector fields in dimension three ⋮ Inverse Jacobian multipliers and Hopf bifurcation on center manifolds ⋮ Integrability of 3-dim polynomial systems with three invariant planes ⋮ Analytic normalization of analytically integrable differential systems near a periodic orbit ⋮ Local integrability of a family of three-dimensional quadratic systems ⋮ Analytic integrability around a nilpotent singularity ⋮ Local integrability of Poincaré-Dulac normal forms ⋮ Generalized involutive symmetry and its application in integrability of differential systems ⋮ On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier ⋮ Varieties and analytic normalizations of partially integrable systems ⋮ Varieties of local integrability of analytic differential systems and their applications ⋮ Regularity and convergence of local first integrals of analytic differential systems ⋮ Orbitally symmetric systems with applications to planar centers ⋮ Reversibility in polynomial systems of ODE's ⋮ Determining ``small parameters for quasi-steady state

Cites Work

• Tikhonov's theorem and quasi-steady state
• Qualitative properties and stabilizability of a model for blood thrombin formation
• A characterization of centres via first integrals
• On differential equations in normal form
• Local theory of nonlinear analytic ordinary differential equations
• On transformations into normal form
• Local first integrals of differential systems and diffeomorphisms
• The Sibirsky component of the center variety of polynomial differential systems.
• Analytic normalization of analytic integrable systems and the embedding flows
• Local analytic integrability for nilpotent centers
• Probleme General de la Stabilite du Mouvement. (AM-17)
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