Sharp large deviations for some hyperbolic systems
  We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincar\'e map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda$ satisfying some additional regularity assumptions. 
Vesselin Petkov and Luchezar Stoyanov
math.DS math-ph math.MP