Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes

Abstract

Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes

Corrigendum to “Differentiating the stochastic entropy in negatively curved spaces under conformal changes”

“…Proof. -The proof of (2.1) copies the proof of Proposition 2.16 in [5], up to the point where one uses (1.2). For P-a.e.…”

“…In this section, we briefly recall the settings and the notations from [5]. We locate the error and introduce the new notations we use.…”

“…With the above notations, the following replaces Proposition 2.16 in [5]: Proposition 2.1. -Let L = ∆ + Y be such that Y * , the dual of Y in the cotangent bundle to the stable foliation over SM , satisfies dY * = 0 leafwisely and pr(− X, Y ) > 0.…”

“…For the proof of Proposition 3.2 in [5], the places that are affected by Proposition 2.16 and should be corrected are as follows: the u 1 , Z 1 t and σ 1 of page 1141 have to be replaced by u * 1 , Z 1, * t and σ * 1 for k * . For Lemma 3.11, the changes are only formal, replacing k 0 v (ω(s), ξ) by k 0, * v (ω(s), ξ) on page 1160 and in the estimate of I 3 .…”

“…There is an error in our paper [5,Proposition 2.16], in the expression of the entropy of a foliated diffusion due to our dismissing the non-symmetry of the diffusions. The main results on the regularities of the entropy (Proposition 3.2 and Theorem 5.1 (ii)) and the structure of their proofs are not affected.…”