The Jacobian Conjecture
I presented a summary of some results
and questions concerning Jacobian Conjectures in August, 2000.
My papers on this topic include:

M. Chamberland, A. Cima, A. Gasull, F. Mañosas,
(2007),
Characterizing Asymptotic Stability with Dulac Functions
,
Discrete and Continuous Dynamical Systems,
17, 5976.

M. Chamberland, (2006),
Dynamics of Maps with
Nilpotent Jacobians,
Journal of Difference Equations and Applications.
12, 4956.

M. Chamberland, J. Llibre and G. Swirszcz (2004),
Weakened MarkusYamabe conditions for
2dimensional global asymptotic stability,
Nonlinear Analysis ,
59 , 951958.

M. Chamberland (2003),
Characterizing Twodimensional Maps whose Jacobians have Constant Eigenvalues,
Canadian Mathematical Bulletin,
46 , 323331

M. Chamberland (2000),
Diffeomorphic RealAnalytic Maps and the Jacobian Conjecture,
Mathematical and Computer Modelling 32, 727732.

M. Chamberland and G.H. Meisters (1998),
A Mountain Pass to the Jacobian Conjecture,
Canadian Mathematical Bulletin
41(5), 442451

M. Chamberland (1998),
Global Asymptotic Stability and the Jacobian Conjecture,
Canadian Applied Mathematical Quarterly
5, 331339.
Several websites have writeups about Jacobian conjectures: