Existence and nonexistence of Puiseux inverse integrating factors in analytic monodromic singularities
Copyright policy )Existence and nonexistence of Puiseux inverse integrating factors in analytic monodromic singularities
AbstractIn this work, we present some criteria about the existence and nonexistence of both Puiseux inverse integrating factors and Puiseux first integrals for planar analytic vector fields having a monodromic singularity. These functions are a wide generalization of their formal or algebraic counterpart in Cartesian coordinates . We prove that none of the functions and can be used to characterize degenerate centers although the existence of is a sufficient center condition.
- Universidade de São Paulo Brazil
- University of Lleida Spain
first integral, Bifurcations of singular points in dynamical systems, center-focus problem, Explicit solutions, first integrals of ordinary differential equations, Bifurcations of limit cycles and periodic orbits in dynamical systems, Inverse integrating factor, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, First integral, Center-focus problem, inverse integrating factor
first integral, Bifurcations of singular points in dynamical systems, center-focus problem, Explicit solutions, first integrals of ordinary differential equations, Bifurcations of limit cycles and periodic orbits in dynamical systems, Inverse integrating factor, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, First integral, Center-focus problem, inverse integrating factor
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