11 citations · 25 across the 7 of their papers we have counts for
7 papers
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…
Normal Hyperbolicity in Secondary Hopf Bifurcations
Pedro C. C. R. Pereira, Douglas D. Novaes
We combine results available in the literature to prove that the torus emerging in a secondary Hopf bifurcation is normally hyperbolic. This result is then applied to establish suf…
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…
On the periodic and antiperiodic aspects of the Floquet normal form
Douglas D. Novaes, Pedro C. C. R. Pereira
Floquet's Theorem is a celebrated result in the theory of ordinary differential equations. Essentially, the theorem states that, when studying a linear differential system with …
Invariant tori via higher order averaging method: existence, regularity, convergence, stability, and dynamics
Douglas D. Novaes, Pedro C. C. R. Pereira
Important information about the dynamical structure of a differential system can be revealed by looking into its invariant compact manifolds, such as equilibria, periodic orbits, a…
A version of Hilbert's 16th Problem for 3D polynomial vector fields: Counting isolated invariant tori
Douglas D. Novaes, Pedro C. C. R. Pereira
Hilbert's 16th Problem, about the maximum number of limit cycles of planar polynomial vector fields of a given degree , has been one of the most important driving forces for new…