arXiv subjects

Magdalena Chmara

Publications and source records attributed to Magdalena Chmara.

3 recordsLinked to original sources

arXiv2024

Bifurcations and invariant sets for a family of replicator maps from evolutionary games

We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of hyperbolic chaos for the considered map. Moreover, we also give a partial solution of an open problem formulated in \cite{Misiurewicz1}: to describe all the one-dimensional maps with all the periodic orbits having the same mean value.

math.DS↗

arXiv2023

Generalized version of the Lions-type lemma

In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz-Sobolev spaces. What matters here is the behavior of the integral, not the space.

math.AP↗

arXiv2018

Mountain pass type periodic solutions for Euler-Lagrange equations in anisotropic Orlicz-Sobolev space

Using the Mountain Pass Theorem, we establish the existence of periodic solution for Euler-Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part $K-W$ and a forcing term. We consider two situations: $G$ satisfying $Δ_2\cap\nabla_2$ in infinity and globally. We give conditions on the growth of the potential near zero for both situations.

math.AP↗