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Symbolic dynamics for the Rössler folded towel map

100%

Zgliczyński P.

tom 47

nr 1

253-258

On stability of forcing relations for multidimensional perturbations of interval maps

63%

Li M.-C. , Zgliczyński P.

Fundamenta Mathematicae

2009

tom 206

nr 1

241-251

We show that all periods of periodic points forced by a pattern for interval maps are preserved for high-dimensional maps if the multidimensional perturbation is small. We also show that if an interval map has a fixed point associated with a homoclinic-like orbit then any small multidimensional perturbation has periodic points of all periods.

Set arithmetic and the enclosing problem in dynamics

63%

Mrozek M. , Zgliczyński P.

2000

tom 74

nr 1

237-259

We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.

Cr-Lohner algorithm

63%

Wilczak D. , Zgliczyński P.

Schedae Informaticae

2011

tom 20

We present a Lohner type algorithm for the computation of rigorous bounds for the solutions of ordinary differential equations and its derivatives with respect to the initial conditions up to an arbitrary order.

Foreword, Contents

32%

Mischaikow K. , Mrozek M. , Zgliczyński P.

tom 47

nr 1

1-7