# American Institute of Mathematical Sciences

October  1999, 5(4): 929-945. doi: 10.3934/dcds.1999.5.929

## Convergence of generic infinite products of homogeneous order-preserving mappings

 1 Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel

Received  August 1998 Revised  June 1999 Published  July 1999

In this paper we establish several results concerning the asymptotic behavior of (random) infinite products of generic sequences of homogeneous order-preserving mappings on a cone in an ordered Banach space. In addition to weak ergodic theorems we also obtain convergence to an operator $f(\cdot)\eta$ where $f$ is a functional and $\eta$ is a common fixed point.
Citation: Simeon Reich, Alexander J. Zaslavski. Convergence of generic infinite products of homogeneous order-preserving mappings. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 929-945. doi: 10.3934/dcds.1999.5.929
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