Transience and multifractal analysis

Godofredo Iommi; Thomas Jordan; Mike Todd

doi:10.1016/j.anihpc.2015.12.007

Transience and multifractal analysis

Godofredo Iommi^*, Thomas Jordan, Mike Todd

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal)

1 Citation (Scopus)

304 Downloads (Pure)

Abstract

We study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show that when the whole system is considered (and not just its recurrent part) the conditional variational principle does not necessarily hold. Moreover, we exhibit an example of a topologically transitive map having discontinuous Lyapunov spectrum. The mechanism producing all these pathological features on the multifractal spectra is transience, that is, the non-recurrent part of the dynamics.

Original language	English
Pages (from-to)	407-421
Number of pages	15
Journal	Annales de l'Institut Henri Poincaré (C) Non Linear Analysis
Volume	34
Issue number	2
Early online date	11 Jan 2016
DOIs	https://doi.org/10.1016/j.anihpc.2015.12.007
Publication status	Published - Mar 2016

Keywords

Ergodic theory
Lyapunov exponents
Multifractal analysis

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10.1016/j.anihpc.2015.12.007

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at 10.1016/j.anihpc.2015.12.007.
Accepted author manuscript, 351 KBLicence: CC BY-NC-ND

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Profiles

Dr Thomas M Jordan

Thomas.Jordan@bristol.ac.uk

Probability, Analysis and Dynamics
School of Mathematics - Senior Lecturer in Pure Mathematics
Pure Mathematics
Ergodic theory and dynamical systems

Person: Academic , Member

Cite this

Iommi, G., Jordan, T., & Todd, M. (2016). Transience and multifractal analysis. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, 34(2), 407-421. https://doi.org/10.1016/j.anihpc.2015.12.007

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