Katrin Gelfert (Max
Planck
Institute,
Dresden)
Lyapunov
exponents on nonconformal repellers - multifractal analysis
Streszczenie:
We investigate the Lyapunov exponents for a
particular
class of nonconformal repellers. Lyapunov exponents are usually only
measureable functions. Thus associated level sets are rarely manifolds
and it is appropriate to use quatities such as the topological entropy
or the Hausdorff dimension to quantify their complexity. In the case of
nonconformal repellers the main difficulty of such an analysis is
related with the possible existence of distinct Lyapunov exponents
associated to different directions, which may change from
point to point. Moreover, the Lyapunov exponents are averages of
nonadditive sequences of functions, and thus neither Birkhoff's ergodic
theorem nor the classical thermodynamic formalism can be used. By means
of a nonadditive topological pressure we establish a version of
multifractal analysis to characterize the topological entropy of each
level set.