Periodic points and dynamic rays of exponential maps.
Evolutionary problems in non-reflexive spaces
Rate-independent problems are considered, where the stored energy density is a function of the gradient. The stored energy density may not be quasiconvex and is assumed to grow linearly. Moreover, arbitrary behaviour at infinity is allowed. In particular, the stored energy density is not required to coincide at infinity with a positively 1-homogeneous function. The existence of a rate-independent process is shown in the so-called energetic formulation.
Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices
Continuing earlier work by Székelyhidi, we describe the topological and geometric structure of so-called -configurations which are the most prominent examples of nontrivial rank-one convex hulls. It turns out that the structure of -configurations in is very rich; in particular, their collection is open as a subset of . Moreover a previously purely algebraic criterion is given a geometric interpretation. As a consequence, we sketch an improved algorithm...
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