78 citations · 159 across the 5 of their papers we have counts for
6 papers
Recent advances in rigorous computation of Poincaré maps
Tomasz Kapela, Daniel Wilczak, Piotr Zgliczyński
In this article we present recent advances on interval methods for rigorous computation of Poincaré maps. We also discuss the impact of choice of Poincaré section and coordinate sy…
CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
Tomasz Kapela, Marian Mrozek, Daniel Wilczak +1
We present the CAPD::DynSys library for rigorous numerical analysis of dynamical systems. The basic interface is described together with several interesting case studies illustrati…
Persistent Homology of Morse Decompositions in Combinatorial Dynamics
Tamal K. Dey, Mateusz Juda, Tomasz Kapela +3
We investigate combinatorial dynamical systems on simplicial complexes considered as {\em finite topological spaces}. Such systems arise in a natural way from sampling dynamics and…
Rigorous KAM results around arbitrary periodic orbits for Hamiltonian Systems
Tomasz Kapela, Carles Simó
We set up a methodology for computer assisted proofs of the existence and the KAM stability of an arbitrary periodic orbit for Hamiltonian systems. We give two examples of applicat…
A Lohner-type algorithm for control systems and ordinary differential inclusions
Tomasz Kapela, Piotr Zgliczyński
We describe a Lohner-type algorithm for the computation of rigorous upper bounds for reachable set for control systems, solutions of ordinary differential inclusions and perturbati…
An existence of simple choreographies for N-body problem - a computer assisted proof
Tomasz Kapela, Piotr Zgliczynski
We consider a question of finding a periodic solution for the planar Newtonian N-body problem with equal masses, where each body is travelling along the same closed path. We provid…