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math.DS2026
Local bifurcations in a class of piecewise-smooth Filippov systems with a nonregular switching curve via a nonlinear double regularization process
Claudio A. Buzzi, Yagor Romano Carvalho
We are interested in analyzing the preservation of bifurcations in a class of piecewise smooth vector fields with a nonregular switching set under a smoothing process that approxim…
math.DS2026
Piecewise Smooth Dynamical Systems Regularized by Convolution
Claudio A. Buzzi, Daniel Panazzolo, Paulo R. da Silva
We present a general regularization procedure for piecewise smooth vector fields whose discontinuity locus is a variety of normal crossings type. We show that such regularization c…
math.DS2024
A note on a recent attempt to solve the second part of Hilbert's 16th Problem
Claudio A. Buzzi, Douglas D. Novaes
For a given natural number , the second part of Hilbert's 16th Problem asks whether there exists a finite upper bound for the maximum number of limit cycles that planar polynomi…