In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.

We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville–Pomeau map.

We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville–Pomeau map.

The question of whether the same acceleration field that is found in a rigid uniformly rotating disc can annul a gravitational field is answered in the negative because their curvatures are different. There is an exact correspondence between a uniformly rotating disc and hyperbolic geometry of constant curvature, while, gravitational fields require non-constant, negative curvature. The connecti...

We prove a Berry–Esseen theorem, local central limit theorem and (local) large (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using existing results the problem is reduced to certain (Young) tower extensions, which main focus of this paper. On towers we will obtain our using contraction proper...