The inverse integrating factor and the Poincaré map
From MaRDI portal
Publication:3574786
DOI10.1090/S0002-9947-10-05014-2zbMath1203.37086arXiv0710.3238MaRDI QIDQ3574786
Maite Grau, Hector J. Giacomini, Isaac A. García
Publication date: 2 July 2010
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0710.3238
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)
Related Items (26)
Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors ⋮ Integrability of vector fields versus inverse Jacobian multipliers and normalizers ⋮ Algebraic Inverse Integrating Factors for a Class of Generalized Nilpotent Systems ⋮ Non-formally integrable centers admitting an algebraic inverse integrating factor ⋮ A survey on the inverse integrating factor ⋮ A class of non-integrable systems admitting an inverse integrating factor ⋮ Nilpotent systems admitting an algebraic inverse integrating factor over \(\mathbb{C}((x,y))\) ⋮ Realization problems for limit cycles of planar polynomial vector fields ⋮ The Poincaré map of degenerate monodromic singularities with Puiseux inverse integrating factor ⋮ The embedding flows of \(C^\infty\) hyperbolic diffeomorphisms ⋮ Existence of inverse Jacobi multipliers around Hopf points in \(\mathbb R^3\): emphasis on the center problem ⋮ Generalized rational first integrals of analytic differential systems ⋮ Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems ⋮ Inverse Jacobian multipliers and Hopf bifurcation on center manifolds ⋮ Existence of inverse integrating factors and Lie symmetries for degenerate planar centers ⋮ Some remarks on inverse Jacobi multipliers around Hopf singularities ⋮ Integral characterization for Poincaré half-maps in planar linear systems ⋮ Center cyclicity for some nilpotent singularities including the ℤ2-equivariant class ⋮ Generalized Hopf bifurcation for planar vector fields via the inverse integrating factor ⋮ Cyclicity of nilpotent centers with minimum Andreev number ⋮ Quasi-homogeneous linearization of degenerate vector fields ⋮ Formal Inverse Integrating Factor and the Nilpotent Center Problem ⋮ Vanishing set of inverse Jacobi multipliers and attractor/repeller sets ⋮ The embedding flow of 3-dimensional locally hyperbolic \(C^\infty\) diffeomorphisms ⋮ Inverse Jacobi Multipliers: Recent Applications in Dynamical Systems ⋮ Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
Cites Work
- Unnamed Item
- Polynomial differential systems having a given Darbouxian first integral
- The loop quantities and bifurcations of homoclinic loops
- On the integrability of two-dimensional flows
- Normalizable, integrable, and linearizable saddle points for complex quadratic systems in \(\mathbb{C}^2\)
- A generalization of Françoise's algorithm for calculating higher order Melnikov functions
- Multiplicity of limit cycles and analytic \(m\)-solutions for planar differential systems
- Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
- Integral invariants and limit sets of planar vector fields
- On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
- On a new type of bifurcation of limit cycles for a planar cubic system
- Finite cyclicity of nontrivial double loops
- On the nonexistence, existence and uniqueness of limit cycles
- HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
- SEMISTABLE LIMIT CYCLES THAT BIFURCATE FROM CENTERS
- Reduction of Singularities of the Differential Equation Ady = Bdx
- On the vanishing set of inverse integrating factors
This page was built for publication: The inverse integrating factor and the Poincaré map
