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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.DS2026
Complex potentials and holomorphic differential equations
Gabriel Rondón, Paulo R. da Silva
A complex potential is a holomorphic function whose real and imaginary parts generate a pair of orthogonal foliations, representing the equipotential…
math.DS2025
On the Piecewise Holomorphic Systems with Three Zones
Carlos Vinicius das Neves Silva, Paulo Ricardo da Silva
We study piecewise-smooth systems with three zones, , whose discontinuity set consists either of a pair of parallel lines or a pair of circles ta…