Dynamical systems approach to 1-d spatiotemporal chaos -- A cyclist's view
Yueheng Lan
Ph D Thesis
School of Physics
Georgia Institute of Technology
Atlanta, GA
* Introduction: From dynamical systems to periodic orbit theory
(95% finished, 8 June 2004)
* Periodic orbit theory
(95% finished, 18 May 2004)
*
Periodic orbits and how to find them
(95% finished, 18 May 2004)
* Complex Ginzburg-Landau equation
(98% finished, 8 June 2004)
* 1-d Kuramoto-Sivashinsky equation and its steady solutions
(95% finished, 8 June 2004)
* Spatiotemporal dynamics
of the 1-d Kuramoto-Sivashinsky equation
(90% finished, 8 June 2004)
* Summary
(90% finished, 18 May 2004)
A
Remarks on the Jacobians for a general flow
(90% finished, 18 May 2004)
B
Comparison of Newton descent with variational principle in
Hamiltonian system
(90% finished, 18 May 2004)
C
Existence of modulated amplitude waves
(90% finished, 18 May 2004)