Spectral decomposition of expanding probabilistic dynamical systems |
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| Affiliation: | 1. Utrecht University, Department of Physical Geography, PO Box 80115, Utrecht, The Netherlands;2. International Centre for Integrated Mountain Development, GPO Box 3226, Kathmandu, Nepal;3. ETH Zurich, Institute of Environmental Engineering, Hydrology and Water Resources Management, Wolfgang-Pauli-Str. 15, 8093 Zurich, Switzerland |
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| Abstract: | We study probabilistic combinations of expanding dynamical systems, which we call expanding probabilistic dynamical systems, in one dimension. If the system is composed by exact endomorphisms we prove that the probabilistic dynamical system is an exact Markov semigroup, and we determine a generalized spectral decomposition of the associated Markov operator on densities for an example of the tent map coupled with the 2-Renyi map. |
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