108 citations · 347 across the 26 of their papers we have counts for
21 papers · 1 filter
Central Configurations with Unequal Masses: Finiteness in Several Exceptional Cases of Five Bodies
Małgorzata Moczurad, Piotr Zgliczyński
We provide a computer-assisted proof of the exact count of classes of central configurations for five bodies for several sets of mass values that are exceptional from the point of…
The number of relative equilibria in the PCR4PB
Jordi-Lluís Figueras, Warwick Tucker, Piotr Zgliczynski
The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial…
Central configurations in planar -body problem with equal masses for
Małgorzata Moczurad, Piotr Zgliczyński
We give a computer assisted proof of the full listing of central configuration for -body problem for Newtonian potential on the plane for with equal masses. We show al…
Beyond the Melnikov method II: multidimensional setting
Maciej J. Capinski, Piotr Zgliczynski
We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds. We do not need to…
Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system
Maciej J. Capinski, Dmitry Turaev, Piotr Zgliczynski
We prove, by employing rigorous numerics, that Shimizu-Morioka system has a Lorenz attractor for an open set of parameter values. Using this result, we prove the existence of a dis…
Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation
Robert Szczelina, Piotr Zgliczyński
We present an algorithm for the rigorous integration of Delay Differential Equations (DDEs) of the form . As an application, we give a computer assisted proof…