33,405 research outputs found
Transience and multifractal analysis
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.Comment: Some updates following referee suggestion
On multidimensional branching random walks in random environment
We study branching random walks in random i.i.d. environment in . For this model, the population size cannot decrease, and a natural
definition of recurrence is introduced. We prove a dichotomy for
recurrence/transience, depending only on the support of the environmental law.
We give sufficient conditions for recurrence and for transience. In the
recurrent case, we study the asymptotics of the tail of the distribution of the
hitting times and prove a shape theorem for the set of lattice sites which are
visited up to a large time
- …