Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898776 | Journal of Differential Equations | 2018 | 18 Pages |
Abstract
We consider the family of dehomogenized Loud's centers Xμ=y(xâ1)âx+(x+Dx2+Fy2)ây, where μ=(D,F)âR2, and we study the number of critical periodic orbits that emerge or disappear from the polycycle at the boundary of the period annulus. This number is defined exactly the same way as the well-known notion of cyclicity of a limit periodic set and we call it criticality. The previous results on the issue for the family {Xμ,μâR2} distinguish between parameters with criticality equal to zero (regular parameters) and those with criticality greater than zero (bifurcation parameters). A challenging problem not tackled so far is the computation of the criticality of the bifurcation parameters, which form a set ÎB of codimension 1 in R2. In the present paper we succeed in proving that a subset of ÎB has criticality equal to one.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
D. Rojas, J. Villadelprat,