Deterministic representation for position-dependent random maps
Deterministic representation for position-dependent random maps
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DOI：
10.3934/dcds.2008.22.529
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发表时间：
2008-08
影响因子：
1.1
通讯作者：
Wael Bahsoun;C. Bose;A. Quas
中科院分区：
文献类型：
--
作者：
Wael Bahsoun;C. Bose;A. Quas
We give a deterministic representation for position dependent random maps and describe the structure of its set of invariant measures. Our construction generalizes the skew product representation of random maps with constant probabilities. In particular, we establish one-to-one correspondence between eigenfunctions corresponding to eigenvalues of unit modulus for the Frobenius-Perron (transfer) operator of the random map and for those of the skew. An immediate consequence is one-to-one correspondence between absolutely continuous invariant measures (acims) for the position dependent random map and acims for its deterministic representation.
