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Let $M$ be a pinched negatively curved Riemannian manifold, whose unittangent bundle is endowed with a Gibbs measure $m_F$ associated to a potential$F$. We compute the Hausdorff dimension of the conditional measures of $m_F$.We study the $m_F$-almost sure asymptotic penetration behaviour of locallygeodesic lines of $M$ into small neighbourhoods of closed geodesics, and ofother compact (locally) convex subsets of $M$. We prove Khintchine-type andlogarithm law-type results for the spiraling of geodesic lines around theseobjects. As an arithmetic consequence, we give almost sure Diophantineapproximation results of real numbers by quadratic irrationals with respect togeneral H\"older quasi-invariant measures.

Logarithm laws for equilibrium states in negative curvature