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BRANCHING PROCESSES AND COMPUTATIONAL COLLAPSE OF DISCRETIZED UNIMODAL MAPPINGS
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systemsdoi:10.1142/s0218127402006229 fatcat:2ctpyxq2urhqtosuzlllkpdgbm