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Oct 10, 2022

Renormalization, fractal geometry, and the Newhouse phenomenon

Date: October 10, 2022 | 11:30 am – 12:30 pm
Speaker: Artur Avila, University of Zurich
Location: Raiffeisen Lecture Hall
Language: English

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As discovered by Poincaré in the end of the 19th century, even small perturbations of very regular dynamical systems may display chaotic features, due to complicated interactions near a homoclinic point. In the 1960s, Smale attempted to understand such dynamics in terms of a stable model, the horseshoe, but this was too optimistic. Indeed, Newhouse showed that even in only two dimensions, a homoclinic bifurcation gives rise to particular wild dynamics, such as the generic presence of infinitely many attractors. This Newhouse phenomenon is associated to a renormalization mechanism, but also with particular geometric properties of some fractal sets within a Smale horseshoe. When considering two-dimensional complex dynamics those fractal sets become much more beautiful but unfortunately also more difficult to handle.

More Information:

Date:
October 10, 2022
11:30 am – 12:30 pm

Speaker:
Artur Avila, University of Zurich

Location:
Raiffeisen Lecture Hall

Language:
English

Contact:

Arinya Eller

Email:
arinya.eller@ist.ac.at

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