ha o - dy n / 99 06 02 5 v 1 1 5 Ju n 19 99 Dynamics near Resonance Junctions in Hamiltonian Systems

ar X iv : c ha o - dy n / 99 11 02 5 v 1 1 8 N ov 1 99 9 General properties of propagation in chaotic systems

We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a Hamiltonian system (a Fermi-Pasta-Ulam chain of oscillators); (ii) a general model for spatio-temporal chaos (the complex Ginzburg-Landau equation); (iii) exp...

ha o - dy n / 98 05 02 1 v 1 2 5 M ay 1 99 8 Passive Tracer Dispersion with Random or Periodic Source ∗

In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration profiles of passive tracers in a two-dimensional shear flow. It is shown that a time-periodic concentration profile exists for time-periodic external source, while for random source, the distribution functions of all concentration profiles weakly converge to a u...

ar X iv : c ha o - dy n / 96 06 01 6 v 1 1 J ul 1 99 6 Hopf ’ s last hope : spatiotemporal chaos in terms of unstable recurrent patterns

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.

ar X iv : c ha o - dy n / 99 10 00 5 v 1 6 O ct 1 99 9 The Finite - Difference Analysis and Time Flow

X iv : c ha o - dy n / 99 10 02 5 v 1 1 8 O ct 1 99 9 Asymptotic expansions of unstable ( stable ) manifolds in time - discrete systems

By means of an updated renormalization method, we construct asymptotic expansions for unstable manifolds of hyperbolic fixed points in the double-well map and the dissipative Hénon map, both of which exhibit the strong homoclinic chaos. In terms of the asymptotic expansion , a simple formulation is presented to give the first homoclinic point in the double-well map. Even a truncated expansion o...