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ON THE SHORTEST DISTANCE BETWEEN ORBITS IN CONFORMAL ITERATED FUNCTION SYSTEMS

Part of: Smooth dynamical systems: general theory Classical measure theory Topological dynamics Ergodic theory

Published online by Cambridge University Press:  11 November 2025

SAISAI SHI Open the ORCID record for SAISAI SHI [Opens in a new window]
SAISAI SHI*
Affiliation:
Anhui University of Finance and Economics , Bengbu, China
*
e-mail: saisai_shi@126.com
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Abstract

Recently, Barros et al. [‘On the shortest distance between orbits and the longest common substring problem’, Adv. Math. 344 (2019), 311–339] adopted a dynamical system perspective to study the decay of the shortest distance between orbits. We calculate the Hausdorff dimensions of the exceptional sets arising from the shortest distance between orbits in conformal iterated function systems.

Keywords

shortest distanceconformal iterated function systemHausdorff dimension

MSC classification

Primary: 37A50: Relations with probability theory and stochastic processes
Secondary: 28A80: Fractals 37B10: Symbolic dynamics 37C45: Dimension theory of dynamical systems

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 11
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

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Footnotes

The work was supported by the National Natural Science Foundation of China (12501109) and the Scientific Research Project of Colleges and Universities in Anhui Province (2024AH050016).

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