arXiv subjects

Marta Kowalczyk

Publications and source records attributed to Marta Kowalczyk.

3 recordsLinked to original sources

arXiv2021

Periodic solutions to symmetric Newtonian systems in neighborhoods of orbits of equilibria

The aim of this paper is to prove the existence of periodic solutions to symmetric Newtonian systems in any neighborhood of an isolated orbit of equilibria. Applying equivariant bifurcation techniques we obtain a generalization of the classical Lyapunov center theorem to the case of symmetric potentials with orbits of non-isolated critical points. Our tool is an equivariant version of the Conley index. To compare the indices we compute cohomological dimensions of some orbit spaces.

math.DS↗

arXiv2018

Symmetric Liapunov center theorem for orbit with nontrivial isotropy group

In this article we prove two versions of the Liapunov center theorem for symmetric potentials. We consider a~second order autonomous system $\ddot q(t)=-\nabla U(q(t))$ in the presence of symmetries of a compact Lie group $Γ$ acting linearly on $\mathbb{R}^n.$ We look for non-stationary periodic solutions of this system in a~neighborhood of an orbit of critical points of the potential $U.$

math.CA↗

arXiv2015

Bifurcations of critical orbits of invariant potentials with applications to bifurcations of central configurations of the N-body problem

In this article we study topological bifurcations of critical orbits of equivariant gradient equations. We give necessary and sufficient conditions for the existence of global bifurcations of solutions of these equations. Moreover, we apply these abstract results to the study of bifurcations of new families of planar central configurations of the N-body problem.

math.CA↗