Fractal Dimension Of Chaotic Saddles in the Kuramoto-Sivashinski Equation

David Sweet, Andamooka
Parvez Guzdar, Institute for Research in Electronics and Applied and Physics(IREAP), University of Maryland

We study the fractal dimension of chaotic saddles -- invariant sets of initial conditions in phase
space responsible for chaotic transient motion -- in the Kuramoto-Sivashinski equation, a 1D PDE that
models the turbulent propagation of a flame front, thin, viscous fluid flow down an inclined plane, and
other physical systems. This PDE can be approximated by a very-high dimensional dynamical system (e.g.,
64, 128, or more dimensions) to which a numerical algorithm recently introduced in [D. Sweet, H. E. Nusse,
J. A. Yorke, Phys. Rev. Lett. 86 2261 (2001)] may be applied to efficiently compute orbits closely
approximating orbits on chaotic saddles present in the systems phase space. A novel simulation method
allows these computations to be performed on a PC rather than a supercomputer.