Unstable periodic orbits in the Lorenz attractor

We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than the more traditional approach of time averaging over a generic orbit. Finally, we discuss the relevance of the present work to the computation of unstable periodic orbits of the driven Navier-Stokes equations, which can be simulated using the lattice Boltzmann method.

Published in:
Philosophical Transactions Of The Royal Society A-Mathematical Physical And Engineering Sciences, 369, 2345-2353
Presented at:
Conference on the Discrete Simulation of Fluid Dynamics (DSFD 2010), Rome, ITALY, Jul 05-08, 2010

 Record created 2011-12-16, last modified 2018-09-13

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