International Symposium on Nonlinear Theory and Its Applications
Pseudo Random Numbers Generated by Dynamical Systems
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One of the most important pseudo random numbers is a van der Corput sequence. We will consider it from the view point of dynamical systems, and show that the discrepancy of pseudo random numbers is deeply connected with the ergodicity of a dynamical system. We first study 1--dimensional cases, and then construct higher dimensional transformations which generate low discrepancy sequences. Main tools are the spectra of Perron--Frobenius operator and renewal equations.