Compactness of Invariant Densities for Families of Expanding, Piecewise Monotonic Transformations
1989 ◽
Vol 41
(5)
◽
pp. 855-869
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Keyword(s):
Let I = [0,1] and let be the space of all integrable functions on I, where m denotes Lebesque measure on I. Let ∥ ∥1 be the ℒ-1-norm and let be a measurable, nonsingular transformation on I. Let denote the space of densities. The probability measure μ is invariant under τ if for all measurable sets A, The measure μ is absolutely continuous if there exists an such that for any measurable set A We refer to ƒ* as the invariant density of τ (with respect to m). It is well-known that ƒ * is a fixed point of the Frobenius-Perron operator defined by
1982 ◽
Vol 2
(2)
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pp. 139-158
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Keyword(s):
1986 ◽
Vol 29
(3)
◽
pp. 367-378
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2014 ◽
Vol 35
(4)
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pp. 1028-1044
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Keyword(s):
1970 ◽
Vol 11
(4)
◽
pp. 417-420
1958 ◽
Vol 10
◽
pp. 222-229
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1968 ◽
Vol 11
(1)
◽
pp. 73-77
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Keyword(s):
1962 ◽
Vol 14
◽
pp. 597-601
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1979 ◽
Vol 31
(6)
◽
pp. 1269-1280
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Keyword(s):