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math.DS2023
New lower bound for the Hilbert number in low degree Kolmogorov systems
Yagor Romano Carvalho, Leonardo P. C. Da Cruz, Luiz F. S. Gouveia
Our main goal in this paper is to study the number of small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point a class of polynomial…
math.DS2023
Holomorphic slow-fast systems
Gabriel Rondón, Paulo R. da Silva, Luiz F. S. Gouveia
In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory w…