Geodesic
Transience and multifractal analysis
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 407-421

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1016/j.anihpc.2015.12.007
Keywords: Multifractal analysis, Ergodic theory, Lyapunov exponents 
@article{AIHPC_2017__34_2_407_0,
     author = {Iommi, Godofredo and Jordan, Thomas and Todd, Mike},
     title = {Transience and multifractal analysis},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {407--421},
     publisher = {Elsevier},
     volume = {34},
     number = {2},
     year = {2017},
     doi = {10.1016/j.anihpc.2015.12.007},
     zbl = {1366.37059},
     mrnumber = {3610938},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.12.007/}
}
TY  - JOUR
AU  - Iommi, Godofredo
AU  - Jordan, Thomas
AU  - Todd, Mike
TI  - Transience and multifractal analysis
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2017
SP  - 407
EP  - 421
VL  - 34
IS  - 2
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.12.007/
DO  - 10.1016/j.anihpc.2015.12.007
LA  - en
ID  - AIHPC_2017__34_2_407_0
ER  - 
%0 Journal Article
%A Iommi, Godofredo
%A Jordan, Thomas
%A Todd, Mike
%T Transience and multifractal analysis
%J Annales de l'I.H.P. Analyse non linéaire
%D 2017
%P 407-421
%V 34
%N 2
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.12.007/
%R 10.1016/j.anihpc.2015.12.007
%G en
%F AIHPC_2017__34_2_407_0
Iommi, Godofredo; Jordan, Thomas; Todd, Mike. Transience and multifractal analysis. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 407-421. doi: 10.1016/j.anihpc.2015.12.007

Cité par Sources :