Roman Srzednicki (Jagiellonian University)
TITLE:
On geometric detection of periodic solutions and chaotic
dynamics of ordinary differential equations
ABSTRACT:
Following ideas of Wazewski and Conley we introduce the notion of
isolating segment, a set of a special form in the extended phase
space of a non-autonomous ordinary differential equation. Under
an additional assumption on time-periodicity of the segment,
we present a theorem on the fixed point index of the Poincare map
associated to the equation.
As consequences, we get a results on the existence of periodic
solutions and results on the existence of symbolic dynamics of
the Poincare map. We illustrate those results by examples of planar
polynomial equations with periodic coefficients.