相关论文: Van der Corput sets in Z^d

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…

We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…

We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of oscillatory Riemann-Hilbert problems associated with partial…

This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.

This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…

A recently introduced model of coupled non linear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns…

These notes present a first graduate course in harmonic analysis. The first part emphasizes Fourier series, since so many aspects of harmonic analysis arise already in that classical context. The Hilbert transform is treated on the circle,…

In this paper we consider the setting of a locally compact, non-complete metric measure space $(Z,d,\nu)$ equipped with a doubling measure $\nu$, under the condition that the boundary $\partial Z:=\overline{Z}\setminus Z$ (obtained by…

We study spatial discretizations of dynamical systems: is it possible to recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of…

This paper is devoted to the study of time-dependent hyperbolic systems and the derivation of dispersive estimates for their solutions. It is based on a diagonalisation of the full symbol within adapted symbol classes in order to extract…

In recent years, "composite" density-functional-theory-based methods comprising specially optimized combinations of functionals, basis sets, and empirical corrections have become widely used owing to their robustness and computational…

We provide a dynamical proof of the van der Corput inequality for sequences in Hilbert spaces that is based on the Furstenberg correspondence principle. This is done by reducing the inequality to the mean ergodic theorem for contractions on…

For partially hyperbolic diffeomorphisms with mostly expanding and mostly contracting centers, we establish a topological structure, called skeleton{a set consisting of finitely many hyperbolic periodic points with maximal cardinality for…

We establish long-time stability of multi-dimensional viscous shocks of a general class of symmetric hyperbolic--parabolic systems with variable multiplicities, notably including the equations of compressible magnetohydrodynamics (MHD) in…

We consider mutually disjoint family of measure preserving transformations $T_1, \cdots, T_k$ on a probability space $(X, \mathcal{B}, \mu)$. We obtain the multiple recurrence property of $T_1, \cdots, T_k$ and this result is utilized to…

In this paper some aspects on the periodic solutions of the extended Duffing-Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated to the extended Duffing-Van der Pol…

We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries small perturbations can lead to large deviations over long times, while…

The multidimensional ($n$-D) systems described by Roesser model are presented in this paper. These $n$-D systems consist of discrete systems and continuous fractional order systems with fractional order $\nu$, $0<\nu<1$. The stability and…

In this project we show the existence of arbitrary length arithmetic progressions in model sets and Meyer sets in the Euclidean $d$-space. We prove a van der Waerden type theorem for Meyer sets. We show that pure point subsets of Meyer sets…

Let $d_N=ND_N(\omega)$ be the discrepancy of the Van der Corput sequence in base $2$. We improve on the known bounds for the number of indices $N$ such that $d_N\leq \log N/100$. Moreover, we show that the summatory function of $d_N$…