7 papers
An affine Birkhoff-Kellogg type result in product spaces and its application to differential systems
Alessandro Calamai, Gennaro Infante, Giuseppe Antonio Veltri
We prove a version of the Birkhoff-Kellogg theorem in product spaces, under affine transformations. This is a fairly natural framework that arises when dealing with parameter-depen…
Birkhoff-Kellogg type results in product spaces and their application to differential systems
Alessandro Calamai, Gennaro Infante, Jorge RodrÃguez-López
We provide a new version of the well-known Birkhoff-Kellogg invariant-direction Theorem in product spaces. Our results concern operator systems and give the existence of component-…
Some contributions on Melnikov chaos for smooth and piecewise-smooth planar systems: "trajectories chaotic in the future"
Alessandro Calamai, Matteo Franca, Michal Pospisil
We consider a -dimensional autonomous system subject to a -periodic perturbation, i.e. We assu…
A new construction for Melnikov chaos in piecewise-smooth planar systems
Alessandro Calamai, Matteo Franca, Michal Pospisil
In this paper we consider a piecewise smooth -dimensional system \[ \dot{\vec{x}}=\vec{g} (\vec{x})+\varepsilon\vec{g}(t,\vec{x},\varepsilon) \] where is a small…
Forced oscillations for generalized -Laplacian equations with Carathéodory perturbations
Alessandro Calamai, Maria Patrizia Pera, Marco Spadini
Using topological methods, we study the structure of the set of forced oscillations of a class of parametric, implicit ordinary differential equations with a generalized -Lapla…
On the dynamics of non-autonomous systems in a~neighborhood of a~homoclinic trajectory
Alessandro Calamai, Matteo Franca, Michal Pospisil
This article is devoted to the study of a -dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that t…