The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...

An asymptotic estimate is given for the coe cients of products of large powers of generating functions. This theorem and another local limit theorem which is useful for conditioning are applied to various combinatorial enumeration problems that involve multivariate Lagrange inversion. 1991 AMS Class. No. Primary: 41A63 Secondary: 05A16, 05C05, 41A60 the electronic journal of combinatorics 6 (19...

Some topics of our twenty some years of joint work is discussed. Just to name a few; joint behavior of the maximum of the Wiener process and its location, global and local almost sure limit theorems, strong approximation of the planar local time difference, a general Strassen type theorem, maximal local time on subsets. AMS 2000 Subject Classification: Primary 60J15, Secondary 60F15, 60J55.

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...