3 papers
math.DS2026
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…
math.DS2025
No infinite spin for partial collisions converging to isolated central configurations on the plane
Anna Gierzkiewicz, Rodrigo G. Schaefer, Piotr ZgliczyÅski
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 …
math.DS2024
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…