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- Piotr Zgliczynski, Konstantin Mischaikow
- Foundations of Computational Mathematics
- 2001

We present a new topological method for the study of the dynamics of dissipative PDEâ€™s. The method is based on the concept of the selfconsistent apriori bounds, which allows to justify rigorously theâ€¦ (More)

We present a topological technique for analyzing dynamical systems with complex behavior, based on the general notion of covering relations. Our method can be used to study multidimensional dynamicalâ€¦ (More)

- Piotr Zgliczynski
- Foundations of Computational Mathematics
- 2004

We present a method of self-consistent a-priori bounds, which allows to study rigorously dynamics of dissipative PDEs. As an application present a computer assisted proof of an existence of aâ€¦ (More)

We describe a Lohner-type algorithm for rigorous integration of dissipative PDEs. Using it for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions we give a computerâ€¦ (More)

- Piotr Zgliczynski
- SIAM J. Applied Dynamical Systems
- 2002

We present a computer assisted proof of the existence of several attracting fixed points for the Kuramotoâ€“Sivashinsky equation ut = (u )x âˆ’ uxx âˆ’ Î½uxxxx, u(x, t) = u(x+ 2Ï€, t), u(x, t) = âˆ’u(âˆ’x, t),â€¦ (More)

- Tomasz Kapela, Piotr Zgliczynski
- 2008

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 perturbations of ODEs.

We present a multidimensional generalization of the SharkovskÄÄ± Theorem concerning the appearance of periodic points for the self-maps on the real line. Introduction Let f : X â†’ X be a map. We sayâ€¦ (More)

- Jacek Cyranka, Piotr Zgliczynski
- SIAM J. Applied Dynamical Systems
- 2015

We prove the existence of globally attracting solutions of viscous Burgersâ€™ equation with periodic boundary conditions on the interval for some particular choices of viscosity and non-autonomousâ€¦ (More)

The restricted circular three-body problem is considered for the following parameter values C = 3.03, Î¼ = 0.0009537 the values for Oterma comet in the Sun-Jupiter system. We present a computerâ€¦ (More)

- Peter Franek, Stefan Ratschan, Piotr Zgliczynski
- Journal of Automated Reasoning
- 2015

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of n equations in n variables, and for which all functions are computable in the sense that itâ€¦ (More)