Transience and multifractal analysis
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 the first 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.
- Publication:
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Annales de L'Institut Henri Poincare Section (C) Non Linear Analysis
- Pub Date:
- March 2017
- DOI:
- 10.1016/j.anihpc.2015.12.007
- arXiv:
- arXiv:1309.0720
- Bibcode:
- 2017AIHPC..34..407I
- Keywords:
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- Mathematics - Dynamical Systems
- E-Print:
- Some updates following referee suggestions