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Inferring symbolic dynamics of chaotic flows from persistence
Gökhan Yalnız, Nazmi Burak Budanur
We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a to…
Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system
Nazmi Burak Budanur, Predrag Cvitanović
Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotati…
Periodic orbit analysis of a system with continuous symmetry - a tutorial
Nazmi Burak Budanur, Daniel Borrero-Echeverry, Predrag Cvitanović
Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In…
Reduction of SO(2) symmetry for spatially extended dynamical systems
Nazmi Burak Budanur, Predrag Cvitanović, Ruslan L. Davidchack +1
Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of…