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.
|Number of pages||15|
|Journal||Annales de l'Institut Henri Poincaré (C) Non Linear Analysis|
|Early online date||11 Jan 2016|
|Publication status||Published - Mar 2016|
- Ergodic theory
- Lyapunov exponents
- Multifractal analysis