This article is from the Nonlinear Science FAQ, by James D. Meiss firstname.lastname@example.org with numerous contributions by others.
Physica D The premier journal in Applied Nonlinear Dynamics
Nonlinearity Good mix, with a mathematical bias
Chaos AIP Journal, with a good physical bent
SIAM J. of Dynamical Systems Online Journal with multimedia
Chaos Solitons and Fractals Low quality, some good applications
Communications in Math Phys an occasional paper on dynamics
Comm. in Nonlinear Sci. New Elsevier journal
and Num. Sim. http://www.elsevier.com/locate/cnsns
Ergodic Theory and Rigorous mathematics, and careful work
International J of lots of color pictures, variable quality.
Bifurcation and Chaos
J Differential Equations A premier journal, but very mathematical
J Dynamics and Diff. Eq. Good, more focused version of the above
J Dynamics and Stability Focused on Eng. applications. New editorial
of Systems board--stay tuned.
J Fluid Mechanics Some expt. papers, e.g. transition to turbulence
J Nonlinear Science a newer journal--haven't read enough yet.
J Statistical Physics Used to contain seminal dynamical systems papers
Nonlinear Dynamics Haven't read enough to form an opinion
Nonlinear Science Today Weekly News: http://www.springer-ny.com/nst/
Nonlinear Processes in New, variable quality...may be improving
Physics Letters A Has a good nonlinear science section
Physical Review E Lots of Physics articles with nonlinear emphasis
Regular and Chaotic Dynamics Russian Journal http://web.uni.udm.ru/~rcd/