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We construct symbolic dynamics for three dimensional flows with positivespeed. More precisely, for each $\chi>0$, we code a set of full measure forevery invariant probability measure which is $\chi$-hyperbolic. These includeall ergodic measures with entropy bigger than $\chi$ as well as all hyperbolicperiodic orbits of saddle-type with Lyapunov exponent outside of$[-\chi,\chi]$. This contrasts with a previous work of Lima & Sarig which builta coding associated to a given invariant probability measure. As anapplication, we code homoclinic classes of measures by suspensions ofirreducible countable Markov shifts.

Symbolic dynamics for large non-uniformly hyperbolic sets of three dimensional flows