Speaker
Description
Dynamical systems theory provides a rigorous framework for studying complex phenomena arising in physics and engineering. A famous example is the Lorenz system, introduced in the 1960s as a simplified model of fluid convection derived from the Navier–Stokes equations. Its solutions, known as Lorenz attractors, became a paradigm of chaotic dynamics and inspired the notion of the “butterfly effect” — small changes in initial conditions can lead to drastically different long-term behavior. Since then, parameterized families of chaotic attractors have been one of the central topics in dynamical systems.
We are particularly interested in the study of planar attractors and the question: which attractors appear typically in certain systems and can they be discovered through physical experiments?
A surprising answer in a particular setting comes from the pseudo-arc. Together with the arc, it is the only planar continuum (that is, a compact connected metric space) in which every proper subcontinuum is homeomorphic to the whole continuum (Hoehn–Oversteegen, 2020). First described about a century ago, the pseudo-arc has remarkable structural properties and arises typically in several topological contexts. In this talk I will present a result which reveals that pseudo-arc is a generic object within natural families of attractors arising as extensions of dynamical systems on interval. This is joint work with Piotr Oprocha (University of Ostrava).
