Related papers: Form discrete- to continuous-time ergodic theorems
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
In quantum logical terms, Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. If interpreted classically those structures serve as graph-theoretic "gadgets" that enforce…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…
We provide an exposition of the proofs of Bourgain's polynomial ergodic theorems. The focus is on the motivation and intuition behind his arguments.
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…
We present implementations of constant-time algorithms for connectivity tests and related problems. Some are implementations of slightly improved variants of previously known algorithms; for other problems we present new algorithms that…
In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…
We prove mean and pointwise ergodic theorems for the action of a discrete lattice subgroup in a connected algebraic Lie group, on infinite volume homogeneous algebraic varieties. Under suitable necessary conditions, our results are…
We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of…
We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a…
We show that with a few modifications the Adomian's method for solving second order differential equations can be used to obtain the known results of the special functions of mathematical physics. The modifications are necessary in order to…
We consider continuous and discrete Schr\"odinger systems with self-adjoint matrix potentials and with additional dependence on time (i.e., dynamical Schr\"odinger systems). Transformed and explicit solutions are constructed using our…
We introduce a non-autonomous generalization of spatial-temporal differentiations, and prove results about probabilistically and topologically generic behaviors of certain spatial-temporal differentiations generated by endomorphisms of…
We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.