Transience and multifractal analysis

Godofredo Iommi*, Thomas Jordan, Mike Todd

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
381 Downloads (Pure)


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 languageEnglish
Pages (from-to)407-421
Number of pages15
JournalAnnales de l'Institut Henri Poincaré (C) Non Linear Analysis
Issue number2
Early online date11 Jan 2016
Publication statusPublished - Mar 2016


  • Ergodic theory
  • Lyapunov exponents
  • Multifractal analysis


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