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Minimal sets in non-smooth dynamical systems


In this project we study the existence of minimal invariant sets in non-smooth dynamical systems. In particular, we are interested in the existence of limit cycles and homoclinic cycles in dimensions $2$ and $3$.In dimension $2$ we focus on the existence of homoclinic cycles for non-smooth systems with two zones, considering the cases saddle-focus and saddle-center (real and virtual). We also want to study the existence of limit cycles for non-smooth dynamical systems with a circle as discontinuity manifold.In dimension $3$ we study the existence of limit cycles and homoclinic orbits in the special case of a model presenting two parallel $T$-singularities. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
LLIBRE, JAUME; MARTINS, RICARDO MIRANDA; TONON, DURVAL JOSE. Limit Cycles of Piecewise Smooth Differential Equations on Two Dimensional Torus. Journal of Dynamics and Differential Equations, v. 30, n. 3, p. 1011-1027, . (15/06903-8)
MARTINS, RICARDO M.; TONON, DURVAL J.. The chaotic behaviour of piecewise smooth differential equations on two-dimensional torus and sphere. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 34, n. 2, p. 356-373, . (15/06903-8)
ANDRADE, K. DA S.; JEFFREY, M. R.; MARTINS, R. M.; TEIXEIRA, M. A.. On the Dulac's problem for piecewise analytic vector fields. Journal of Differential Equations, v. 266, n. 4, p. 2259-2273, . (13/07523-9, 18/03338-6, 12/18780-0, 15/06903-8, 14/21259-5)

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