We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of N , N ≥ 2, symbols and with C1 diffeomorphisms of the circle as fiber maps. The systems we study are transitive and genuinely nonhyperbolic, exhibiting simultaneously ergodic measures with positive, negative, and zero exponents. We derive a multifractal analysis for the topological entropy of the level sets...

We argue that the configurations of maximal entropy in five-dimensional asymptotically flat vacuum gravity, for fixed mass and angular momentum, are ‘black Saturns’ with a central, close to static, black hole and a very thin black ring around it. For any value of the angular momentum, the upper bound on the entropy is equal to the entropy of a static black hole of the same total mass. For fixed...

For $n$-dimensional Riemannian manifolds $M$ with Ricci curvature bounded below by $-(n-1)$, the volume entropy is above $n-1$. If compact, it known that equality holds if and only hyperbolic. We extend this result to $\mathsf{RCD}^{\ast}(-(N-1),N)$ spaces. While upper bound straightforward, rigidity case quite involved due lack of a smooth structure in $\mathsf{RCD}^{\ast}$ As an application w...

Given a compact topological dynamical system $(X, f)$ with positive entropy and upper semicontinuous map, any closed invariant subset $Y \subset X$ entropy, we show that there exists continuous roof function such the set o

We show that a transient graph can be extended to a recurrent graph of equal entropy which is either positive recurrent of null recurrent, and we give an example of each type. We extend the notion of local entropy to topological Markov chains and prove that a transitive Markov chain admits a measure of maximal entropy (or maximal measure) whenever its local entropy is less than its (global) ent...

We exploit the idea to use maximal-entropy method, successfully tested in information theory and statistical thermodynamics, determine approximating function's coefficients squared errors' weights simultaneously as output of one single problem least-square approximation. provide evidence method's capabilities performance through its application representative test cases by working with polynomi...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...