30 citations · 46 across the 5 of their papers we have counts for
7 papers
Existence of a cylinder foliated by periodic orbits in the generalized Chazy differential equation
Jaume Llibre, Douglas D. Novaes, Claudia Valls
The generalized Chazy differential equation corresponds to the following two-parameter family of differential equations \begin{equation*}\label{gcdeq} \dddot x+|x|^q \ddot x+\dfrac…
A note on the conjecture
J. Llibre, C. Valls
Let be a map from the set of positive integers into itself defined as follows: Let be a positive integer. If is odd, then , and if is even, then $g(x)=x/…
Zero-Hopf bifurcation in the general Van der Pol-Duffing equation
Murilo Cândido, Claudia Valls
We study analytically the coexistence of multiple periodic solutions and invariant tori in the general Van der Pol-Duffing oscillator equations. We use several results related to t…
Periodic solutions and invariant torus in the Rössler System
Murilo R. Cândido, Douglas D. Novaes, Claudia Valls
The Rössler System is characterized by a three-parameter family of quadratic 3D vector fields. There exist two one-parameter families of Rössler Systems exhibiting a zero-Hopf equi…
Admissibility and nonuniformly hyperbolic sets
Luis Barreira, Davor Dragicevic, Claudia Valls
We obtain a characterization of two classes of dynamics with nonuniformly hyperbolic behavior in terms of an admissibility property. Namely, we consider exponential dichotomies wit…
Integrability of the Hide--Skeldon--Acheson dynamo
Adam Mahdi, Claudia Valls
In this work we consider the Hide-Skeldon-Acheson dynamo model \[ \dot x=x(y-1)-βz, \quad \dot y =α(1-x^2)-κy, \quad \dot z =x-λz, \] where and are parameters. We contr…
A rigorous implementation of the Jeans--Landau--Teller approximation
G. Benettin, A. Carati, G. Gallavotti
Rigorous bounds on the rate of energy exchanges between vibrational and translational degrees of freedom are established in simple classical models of diatomic molecules. The resul…