Piotr Zgliczynski

Daniel Wilczak, Piotr Zgliczynski

The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of ODEs generating nontrivial dynamics, for the parameter range containing two period doubling bifurcations.

Daniel Wilczak, Piotr Zgliczynski

We present a topological method for the efficient computer assisted verification of the existence of the homoclinic tangency which unfolds generically in a one-parameter family of planar maps. The method has been applied to the Henon map and the forced damped pendulum ODE.