15 citations · 15 across the 7 of their papers we have counts for
9 papers
Generalization of Lyapunov Center Theorem for Hamiltonian systems via normal forms theory
A. Gołębiewska, S. Rybicki
In this article we formulate and prove sufficient conditions for the existence of trajectories of nonstationary periodic solutions of autonomous Hamiltonian systems in a neighbourh…
Bifurcation of closed orbits from equilibria of Newtonian systems with Coriolis forces
Anna Gołȩbiewska, Ernesto Pérez-Chavela, Sławomir Rybicki +1
We consider autonomous Newtonian systems with Coriolis forces in two and three dimensions and study the existence of branches of periodic orbits emanating from equilibria. We inves…
Connected sets of solutions of symmetric elliptic systems
Anna Gołębiewska, Sławomir Rybicki, Piotr Stefaniak
The purpose of this paper is twofold. First we study bifurcations of connected sets of critical orbits of some invariant functional from a given family of critical orbits. We use t…
Symmetric Liapunov center theorem for orbit with nontrivial isotropy group
Marta Kowalczyk, Ernesto Pérez-Chavela, Sławomir Rybicki
In this article we prove two versions of the Liapunov center theorem for symmetric potentials. We consider a~second order autonomous system in the pres…
Symmetric Liapunov center theorem for minimal orbit
Ernesto Pérez-Chavela, Sławomir Rybicki, Daniel Strzelecki
Using the techniques of equivariant bifurcation theory we prove the existence of non-stationary periodic solutions of -symmetric systems in any neig…
Rabinowitz alternative for non-cooperative elliptic systems on geodesic balls
Sławomir Rybicki, Naoki Shioji, Piotr Stefaniak
The purpose of this paper is to study properties of continua (closed connected sets) of nontrivial solutions of non-cooperative elliptic systems considered on geodesic balls in $S^…