We show that the Poincaré return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.
@article{hal-00113005,
author = {Saussol, B. and Troubetzkoy, S. and Vaienti, S.},
title = {Recurrence, dimensions and Lyapunov exponents},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00113005}
}
Saussol, B.; Troubetzkoy, S.; Vaienti, S. Recurrence, dimensions and Lyapunov exponents. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00113005/