Cyclicity of a fake saddle inside the quadratic vector fields
Copyright policy )Cyclicity of a fake saddle inside the quadratic vector fields
Agraïments: The first author acknowledges the support of FWO Vlaanderen (Grant number G093910). UNAB10-4E-378 grants This paper concerns the study of small-amplitude limit cycles that appear in the phase portrait near an unfolded fake saddle singularity. This degenerate singularity is also known as a impassable grain. The normal form of the unperturbed vector field is like a degenerate flow box. Near the singularity,the phase portrait consists of parallel fibers, all of which but one have no singular points, and at the singular fiber, there is one node. We study different techniques in order to show that the cyclicity is bigger or equal than two when the normal form is quadratic.
- Hasselt University Belgium
- Autonomous University of Barcelona Spain
- Centre de Recerca Matemàtica Spain
Cyclicity; Fake saddle; Impassable grain; Limit cycle; Bifurcation; Singularity unfolding, Bifurcations of singular points in dynamical systems, Bifurcation theory for ordinary differential equations, Fake saddle, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, fake saddle, cyclicity, limit cycle, Bifurcations, Limit cycles, Bifurcations of limit cycles and periodic orbits in dynamical systems, bifurcation, cyclicity; fake saddle; impassable grain; limit cycle; bifurcation; singularity unfolding, impassable grain, Cyclicity, Impassable grain, Singular perturbations of ordinary differential equations
Cyclicity; Fake saddle; Impassable grain; Limit cycle; Bifurcation; Singularity unfolding, Bifurcations of singular points in dynamical systems, Bifurcation theory for ordinary differential equations, Fake saddle, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, fake saddle, cyclicity, limit cycle, Bifurcations, Limit cycles, Bifurcations of limit cycles and periodic orbits in dynamical systems, bifurcation, cyclicity; fake saddle; impassable grain; limit cycle; bifurcation; singularity unfolding, impassable grain, Cyclicity, Impassable grain, Singular perturbations of ordinary differential equations
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