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• #### RANK ONE DYNAMICS NEAR HETEROCLINIC CYCLES AND CONDITIONAL MEMORY LOSS FOR NONEQUILIBRIUM DYNAMICAL SYSTEMS ﻿

(2013-08)
There are two parts in this dissertation. In the first part we prove that genuine nonuniformly hyperbolic dynamics emerge when flows in $\mbb{R}^{N}$ with homoclinic loops or heteroclinic cycles are subjected to certain ...
• #### Smooth Infinitesimal Rigidity for Higher Rank Partially Hyperbolic Actions on Step-2 Nilmanifolds ﻿

(2012-05)
If Λ is finitely generated and M is compact, an action φ M → M is a C ∞ homomorphism : Λ ×from Λ to Diff(M ). There is a natural formal tangent space at the point [φ] determined by φ, which is given by the 1-cocycles ...