Does the hyperbolicity of periodic orbits of a geodesic flow without conjugate points imply the Anosov property?

About the Measure of Maximal Entropy and Horospherical Foliations of Geodesic Flows of Compact Manifolds Without Conjugate Points

“…Thus, uniform divergence of radial Jacobi fields implies uniform divergence of geodesic rays. This is proposition 3.6 of [17].…”

“…If T (θ, A) does not depend on θ, we say that radial Jacobi fields diverge uniformly. We next restate Theorem 3.1 of Ruggiero's work [17].…”

“…Thus there are several works that use the result or deal with things related to it. Among them, in the context of geodesic flows we can cite some due to Paternain [80], Barbosa-Ruggiero [81], Ruggiero [17], Ledrappier-Lima-Sarig [82] and Araujo-Lima-Poletti [83]. Thus, to apply Theorem 4.3, let us look at Liouville measure restricted to R 1 .…”

“…As said in the introduction, we rely on a Ruggiero's Theorem (Theorem 4.1 of [17]) which we restate below. Theorem 4.2.…”

“…We pursue the extension of this conclusion to our higher dimensional context under an additional local assumption given in Chapter 4. Finally, we want to show some dynamical consequences of Ruggiero's work [17] in our context. Specifically, about some set closely related to Pesin set and the hyperbolic periodic points of the geodesic flow.…”