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The Perron-Frobenius operator in spaces of smooth functions on an interval

Published online by Cambridge University Press:  19 September 2008

B. Szewc
B. Szewc
Affiliation:
SGGW-Warsaw Agricultural University, Institute of Applied Mathematics and Statistics, Warsaw, Poland
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Abstract

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The densities of invariant measures for Misiurewicz maps and Lasota-Yorke maps of class Cr are of class Cr-1 on certain intervals (forming the partition of an interval in case of Misiurewicz maps). For these maps the Perron-Frobenius operator has an unambiguous decomposition into the sum of projections onto eigenspaces (multiplied by the eigenvalues) and a remainder operator. The remainder operator has spectral radius less than one in certain spaces of smooth functions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 4 , December 1984 , pp. 613 - 643
Copyright
Copyright © Cambridge University Press 1984

References

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