Generalized continued fractions

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The invariant measures for the transformations x bar right arrow {phi(x)} on the unit interval are studied where (i) phi is an element of C-2, (ii) phi' < 0, (iii) phi(0+) = +infinity, phi(1)= 1, (iv) the map x bar right arrow {phi(x)} is eventually expansive, and (v) phi' and phi " satisfy some growth conditions. It is shown that the invariant ergodic measure rho(x) dx satisfies rho(0) = (1 - 1/phi'(1)) . rho(1). For phi(x) = 1/x(p), the limiting behavior of rho is investigated as p --> +infinity or p --> p(0) = 0.241485... (C) 2000 Elsevier Science Inc. All rights reserved. AMS classification. Primary 28C10; 58F11.
Publisher
ELSEVIER SCIENCE INC
Issue Date
2000-03
Language
English
Article Type
Article
Keywords

INVARIANT MEASURES; INTERVAL; MAPS

Citation

APPLIED MATHEMATICS AND COMPUTATION, v.109, no.2-3, pp.287 - 299

ISSN
0096-3003
URI
http://hdl.handle.net/10203/70493
Appears in Collection
MA-Journal Papers(저널논문)
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