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A list of official collaborators includes: J. C. Sprott, J. P. Crutchfield, N. Ay, Yuzuru Sato, F. Atay, J. R. Albers, W. D. Dechert, and C. R. Shalizi.
A list of unofficial collaborators: Juergen Jost, Moe Hirsch, Keith Burns, Buz Brock, Ian Dobson, Carl McTague, Jodi Supanich
These lists are far from being exhaustive...
Institutes: IHES in France, IMPA in Brazil, Warwick dynamical systems, SFI in Santa Fe, PSCS in Michigan, IMA at U. Minnesota, CDSNS at Georgia Tech, Center for Dynamical Systems at Penn State, Center for Nonlinear Dynamics at UT Austin
Groups: Information Theory of Cognitive Systems Group, Dynamics of learning at UC Davis.
Departments: Madison Math, Madison Physics, Northwestern, ASU, UC Davis Math, Rutgers Math, Maryland Chaos
Preprint servers: IMPA, general arXiv, math arXiv Santa Fe Institute working papers
Popular journals: Nonlinearity, Chaos, Physica D
A good math dictionary PlanetMath
A good statistics dictionary Steps
Friends, Advisors, Collaborators, and Rockstars (in no particular order):
PhD advisors: Clint Sprott and Jim Crutchfield
Dynamics rockstars: Keith Burns, David Ruelle, Amie Wilkinson, Joel Robbin, Karl Peterson (Ok this is a terrible list, I have started to just use my bookmarks for people.)
Bifurcation theory rockstars: Yuri Kuznetsov
Numerical mathematics rockstars: Alan Edelman