We study the regularity of entropy spectrum Lyapunov exponents for hyperbolic maps on surfaces. It is well-known that a concave upper semi-continuous function which analytic interior set exponents. In this paper we construct family horseshoes with discontinuous at boundary

The purpose of this paper is to characterize the Banach spaces and the locally convex spaces E for which bounded additive measures or bounded σadditive measures with values in L(E, F ), the space of continuous linear maps from E into F , are of bounded semi-variation for any Banach space or locally convex space F . This paper gives an answer to a problem posed by D.H. Tucker in [6].

In this article, we investigate sufficient conditions for controllability of second-order semi-linear damped neutral functional initial value problem for the class of differential inclusions in Banach spaces using the theory of strongly continuous cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. An example is provided to illustrate the result. This work i...