4 papers
No infinite spin for total collisions in the spatial N-body problem
Gabriella Pinzari, Piotr Zgliczynski
In the -body problem, when bodies tend to a total collision, then its normalized shape curve converges to the set of normalized central configurations, which has symmetr…
Polynomial normal forms for ODEs near a center-saddle equilibrium point
Amadeu Delshams, Piotr Zgliczynski
In this work we consider a saddle-center equilibrium for general vector fields as well as Hamiltonian systems, and we transform it locally into a polynomial normal form in the sadd…
No infinite spin for partial collisions converging to isolated central configurations on the plane
Anna Gierzkiewicz, Rodrigo G. Schaefer, Piotr Zgliczyński
In the -body problem, when a~cluster of bodies tends to a collision, then its normalized shape curve converges to the set of normalized central configurations, which has …
Shadowing of non-transversal heteroclinic chains in lattices
Amadeu Delshams, Piotr Zgliczynski
We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspir…