Speaker: Eran Igra (SIMIS)
Time: 2025-09-22 16:00:00
Venue: R1310
Zoom Meeting ID: 844 0594 7424 (Passcode: 076895)
Abstracts:
One (useful) way to study three dimensional chaotic attractors is to define interval maps which behave similarly (and are often and are easier to analyze qualitatively), and then compare their dynamics and bifurcations with the numerical studies of the Differential Equation. Of course, chaotic attractors are not one-dimensional maps suspended in 3D, which raises an interesting question – can we explain analytically why their dynamics and bifurcations are described so well by one-dimensional maps? In this talk we will answer this question for the Lorenz attractor, one of the most famous paradigms of chaos. As we will prove, one can rigorously reduce the butterfly attractor into a one-dimensional interval map which captures all its essential dynamics. Following that, using renormalization theory we will prove how one can use these results to provide “topological lower bounds” for the possible complexity of knots realized as periodic orbits on the attractor. Based on a joint work with Łukasz Cholewa.
Introduction to the speaker: Dr. Eran Igra is a Postdoctoral scholar at the SIMIS. Previously, he completed his PhD under the supervision of Prof. Tali Pinsky at the Technion – Israel Institute of Technology. His interests are in the dynamics and bifurcations of three-dimensional flows, homeomorphisms on manifolds, and related topics.
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