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CONTINUITY OF THE HAUSDORFF DIMENSION FOR GRAPH-DIRECTED SYSTEMS

Part of: Smooth dynamical systems: general theory Complex dynamical systems Special classes of linear operators Classical measure theory

Published online by Cambridge University Press:  16 August 2016

AMIT PRIYADARSHI
AMIT PRIYADARSHI*
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India email priyadarshi@maths.iitd.ac.in
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Abstract

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In this paper we discuss the continuity of the Hausdorff dimension of the invariant set of generalised graph-directed systems given by contractive infinitesimal similitudes on bounded complete metric spaces. We use the theory of positive linear operators to show that the Hausdorff dimension varies continuously with the functions defining the generalised graph-directed system under suitable assumptions.

Keywords

Hausdorff dimensiongraph-directed systemsiterated function systemspositive operatorsspectral radius

MSC classification

Primary: 37F35: Conformal densities and Hausdorff dimension
Secondary: 28A80: Fractals 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems 47B65: Positive operators and order-bounded operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 3 , December 2016 , pp. 471 - 478
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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