78 citations · 152 across the 12 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…
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…