Charles Walkden

University of Manchester

Stability Index and Weierstrass Functions

Ergodic Theory and Dynamical Systems Seminar

12th March 2020, 2:00 pm – 3:00 pm
Fry Building, 2.04

A dynamical system may have multiple attractors. The basin of attraction for a given attractor is the set of points which, under iteration, converge to that attractor. In the case where there are multiple attractors, the basins may have very complicated local structure, for example the boundary between them could be highly irregular. The stability index (introduced numerically by Alexander-Yorke-You-Kan, Sommerer-Ott and others in physical systems in the early 1990s and studied more theoretically by Podvigina-Ashwin (2011) and Keller (2015, 2017)) is a number, behaving like a local dimension, that captures the complexity of the local structure of the basins of attraction. This talk will discuss how one can explicitly calculate the stability index in the case of skew-product dynamical systems, using classical tools and techniques from hyperbolic dynamics and thermodynamic formalism.

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