Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

The book aims to provide a global perspective of this theory and make it easier for the
reader to digest the growing literature on this subject. This is not the first book on the subject …

We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems:
namely those modelled by Young towers with summable decay of correlations. In the case of …

We obtain results on large deviations for a large class of nonuniformly hyperbolic dynamical
systems with polynomial decay of correlations $1/n^\beta $, $\beta> 0$. This includes …

We introduce a gluing orbit property, weaker than specification, for both continuous maps
and flows. We prove that flows with the C 1-robust gluing orbit property are uniformly …

We show some level-2 large deviation principles for rational maps satisfying a strong form of
non-uniform hyperbolicity, called 'Topological Collet–Eckmann'. More precisely, we prove a …

Over the last 10 years or so, advanced statistical properties, including exponential decay of
correlations, have been established for certain classes of singular hyperbolic flows in three …

We obtain large deviation bounds for non-uniformly expanding maps with non-flat
singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting …

We construct open sets of C k (k≥ 2) vector fields with singularities that have robust
exponential decay of correlations with respect to the unique physical measure. In particular …

We obtain a exponential large deviation upper bound for continuous observables on
suspension semiflows over a non-uniformly expanding base transformation with non-flat …