Atmosphere Ocean Science Friday Seminar

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<s>Periodic orbits</s> n-tori and where to find them

Speaker: Claire Valva, CAOS

Location: Warren Weaver Hall 1314

Date: Friday, December 1, 2023, 4 p.m.

Synopsis:

We can understand the statistical properties of the chaotic dynamics of turbulence is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system’s chaotic attractor, such as periodic orbits or invariant tori which capture quasi-periodic dynamics. As such, we are interested in finding ways to both detect and (numerically) converge these objects. In this talk, I will give an overview of periodic orbit n-tori theory and its applications to studying turbulence, and then present a method for generating guesses for invariant tori by processing turbulent data using dynamic mode decomposition (DMD). I will discuss examples including an implementation of this method where we find 2-tori from the Kuramoto-Sivashinsky equation in a chaotic regime.