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Finite approximation for the Frobenius-Perron operator. A solution to Ulam’s conjecture. (English) Zbl 0357.41011


MSC:

41A35 Approximation by operators (in particular, by integral operators)
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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[1] Gantmacher, F.R, ()
[2] {\scT. Y. Li and J. A. Yorke}, Ergodic transformations from an interval into itself, submitted for publication. · Zbl 0371.28017
[3] Halmos, P, Lecture on ergodic theory, (1956), Chelsea Publiching New York · Zbl 0073.09302
[4] Kemeny, J; Mirkil; Snell; Thompson, Finite mathematics structures, (1960), Prentice-Hall Englewood Cliffs, N.J
[5] Lasota, A; Yorke, J.A, On the existence of invariant measures for piecewise monotomic transformations, Trans. amer. math. soc., 186, 481-488, (1973) · Zbl 0298.28015
[6] Natanson, I.P, Theory of functions of real variable, (1961), Ungar New York · Zbl 0064.29102
[7] Rechard, O, Invariant measures for many-one transformations, Duke math. J., 23, 477-488, (1956) · Zbl 0070.28001
[8] Ulam, S, Problems in modern mathematics, (1960), Interscience Publishers New York · Zbl 0137.24201
[9] Lasota, A, Relaxation oscillations and turbulence, ordinary differential equations, () · Zbl 0353.34040
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