440 citations · 1.3k across the 26 of their papers we have counts for
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Minimal cover of high-dimensional chaotic attractors by embedded recurrent patterns
Daniel L. Crane, Ruslan L. Davidchack, Alexander N. Gorban
We propose a general method for constructing a minimal cover of high-dimensional chaotic attractors by embedded unstable recurrent patterns. By minimal cover we mean a subset of av…
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…
On the use of stabilising transformations for detecting unstable periodic orbits in the Kuramoto-Sivashinsky equation
Jonathan J. Crofts, Ruslan L. Davidchack
In this paper we develop further a method for detecting unstable periodic orbits (UPOs) by stabilising transformations, where the strategy is to transform the system of interest in…
On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain
Predrag Cvitanović, Ruslan L. Davidchack, Evangelos Siminos
The continuous and discrete symmetries of the Kuramoto-Sivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its chaot…
Efficient detection of periodic orbits in chaotic systems by stabilising transformations
Jonathan J Crofts, Ruslan L Davidchack
An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelche…