23 Feb 2005; Mat-Nat Faculty (UITO), room U1. Wednesday 10:15-12:00

Martin Rypdal "Calculation of Entropy via Multiplicity"

The talk will be about topological entropy of piecewise affine maps. I will introduce the notions of singularity entropy, multiplicity entropy and show their relations to the topological entropy. I will also introduce differentials of piecewise affine maps and show how this can be used to prove a result for piecewise affine maps of skew product type. Namely the following result (joint with B.Kruglikov) will be explained:

h_{top}(S) ≤h_{top}(SxT)≤h_{top}(S)+h_{mult}(S),

where the piece-wise affine map SxT is the skew product over a map S and all the maps {z}xT are piece-wise affine contracting. The notation h_{mult} means multiplicity entropy. The above formula has also an analog for the measure entropy. Some non-trivial corollaries will be deduced.