Invariant measures ofC
2-diffeomorphisms of Markov type inR
d |
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Authors: | Piotr Bugiel |
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Institution: | (1) Department of Mathematics, Jagellonian University, ul. Reymonta 4, PL-30-059 Kraków, Poland |
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Abstract: | A class of uniformly expanding, piecewiseC
2-diffeomorphisms from domainsIR
d
(bounded or not) into themselves is considered. It is shown that the number of the extreme points of Fix (P
)={gG:Pg=g} whereP
is the Frobenius-Perron operator associated with andG={gL
1: g0 g=1}, can be determined in an effective way. Moreover, it is shown that the sequence {P
j
g} is convergent inL
1 for anygG, and in the topology of uniform convergence for anygG(1). The limit is a linear projectionR inL
1 (defined by (3.1)) which mapsG onto Fix (P
) (see Th. 3.1).Dedicated to professor A. Lasota on the occasion of his 60th birthday |
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Keywords: | |
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