15 papers · 1 filter
Hopf-like bifurcations induced by hysteresis and time-delay near monodromic tangential singularities
Douglas D. Novaes, Paulo Santana, David J. W. Simpson
We investigate planar piecewise-analytic vector fields, focusing on the merged focus and other monodromic tangential singularities when hysteresis or time-delay is incorporated int…
Weakly Normally Hyperbolic Invariant Tori: Persistence and an Averaging Principle
Douglas D. Novaes, Pedro C. C. R. Pereira
We prove a persistence theorem for attracting weakly normally hyperbolic invariant tori under small time-periodic perturbations. The theorem extends recent continuation results for…
Infinite-Piecewise Expanding Maps: Chaos, Ergodicity and Invariant-Set Complexity
Matheus G. C. Cunha, Douglas D. Novaes, Gabriel Ponce
In this paper, we study a class of one-dimensional piecewise maps defined by infinitely many smooth expanding branches. This class arises naturally in the context of non-smooth dyn…
Growth estimate for the number of crossing limit cycles in planar piecewise polynomial vector fields
Luana Ascoli, Douglas D. Novaes
Motivated by the classical Hilbert's Sixteenth Problem, we extend some main developments obtained for Hilbert's number in the polynomial setting to the piecewise polynomial context…
Detecting Limit Tori in Non-Smooth Systems: An Analytic Approach with Applications to 3D Piecewise Linear Systems
Murilo R. Cândido, Douglas D. Novaes, Joan S. G. Rivera
This work investigates a class of non-autonomous -periodic piecewise smooth differential systems and their associated time- maps. Our main result provides an analytical appro…
Averaging theory and catastrophes
Pedro C. C. R. Pereira, Mike R. Jeffrey, Douglas D. Novaes
When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order "guiding system", placing the time dependen…