37D05 Hyperbolic orbits and sets 
37D10 Invariant manifold theory 
37D15 Morse-Smale systems 
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D30 Partially hyperbolic systems and dominated splittings 
37D35 Thermodynamic formalism, variational principles, equilibrium states 
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37D45 Strange attractors, chaotic dynamics 
37D50 Hyperbolic systems with singularities (billiards, etc.)
37D99 None of the above, but in this section