78 citations · 152 across the 12 of their papers we have counts for
16 papers
Central configurations on the plane with heavy and light bodies
Małgorzata Moczurad, Piotr Zgliczyński
We study the problem of planar central configurations with heavy bodies and bodies with arbitrary small masses. We derive the equation which describe the limit of light mas…
From the Sharkovskii theorem to periodic orbits for the Rössler system
Anna Gierzkiewicz, Piotr Zgliczyński
We extend Sharkovskii's theorem to the cases of -dimensional maps which are close to 1D maps, with an attracting -periodic orbit. We prove that, with relatively weak topologi…
Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem
Maciej J. Capiński, Marcel Guardia, Pau Martín +2
Consider the Restricted Planar Circular 3 Body Problem with both realistic mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence of all possible combinati…
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…
Periodic orbits in Rössler system
Anna Gierzkiewicz, Piotr Zgliczyński
We prove the existence of -periodic orbits for almost all in the Rössler system with attracting periodic orbit, for two sets of parameters. The proofs are compu…
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…
Rigorous FEM for 1D Burgers equation
Piotr Kalita, Piotr Zgliczyński
We propose a method to integrate dissipative PDEs rigorously forward in time with the use of Finite Element Method (FEM). The technique is based on the Galerkin projection on the F…
A computer-assisted proof of symbolic dynamics in Hyperion's inner rotation model
Anna Gierzkiewicz, Piotr Zgliczyński
The rotation of Hyperion is often modelled by equations of motion of an ellipsoidal satellite. The model is expected to be chaotic for large range of parameters. The paper contains…
Symbolic dynamics for Kuramoto-Sivashinsky PDE on the line --- a computer-assisted proof
Daniel Wilczak, Piotr Zgliczyński
The Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter is considered. We give a computer-assisted proof the existence of s…
Shadowing of non-transversal heteroclinic chains
Amadeu Delshams, Adrià Simon, Piotr Zgliczyński
We present a new result about the shadowing of nontransversal chain of heteroclinic connections based on the idea of dropping dimensions. We illustrate this new mechanism with seve…
Hyperbolicity and Averaging for the Srzednicki-Wójcik equation
Piotr Zgliczyński
For the Srzednicki-Wójcik equation, the planar nonautonomous ODE parameterized by , using av…
Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Fast Oscillating Forces
Jacek Cyranka, Piotr B Mucha, Edriss S Titi +1
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time extern…
Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing
Aleksander Czechowski, Piotr Zgliczyński
We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of…
On rigorous estimates of eigenspaces and eigenvalues of a matrix
Łukasz Struski, Jacek Tabor, Piotr Zgliczyński
We present a method of cones for rigorous estimations of eigenvectors, eigenspaces and eigenvalues of a matrix. The key notion is the cone-domination and is inspired by ideas from…
Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations
Jacek Cyranka, Piotr Zgliczyński
We describe a topological method to study the dynamics of dissipative PDEs on a torus with rapidly oscillating forcing terms. We show that a dissipative PDE, which is invariant wit…
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…