Related papers: Lower bounds for the dynamically defined measures

A compatible point-shift $F$ maps, in a translation invariant way, each point of a stationary point process $\Phi$ to some point of $\Phi$. It is fully determined by its associated point-map, $f$, which gives the image of the origin by $F$.…

In this paper, given a topological space $X$, an interval $I\subseteq {\bf R}$ and five continuous functions $\varphi, \psi, \omega :X\to {\bf R}$, $\alpha, \beta:I\to {\bf R}$, we are interested in the infimum of the function $\Phi:X\to…

Let $f:M\rightarrow M$ be a $C^1$ diffeomorphism with a dominated splitting on a compact Riemanian manifold $M$ without boundary. We state and prove several sufficient conditions for the topological entropy of $f$ to be positive. The…

We consider an action which consists of two terms: the first S_{1}=\int L_{1}\Phi d^{4}x and the second S_{2}=\int L_{2}\sqrt{-g}d^{4}x where \Phi is a measure which has to be determined dynamically. S_{1} satisfies the requirement that the…

In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical…

In a Hilbert space $\mathcal H$, we study the asymptotic behaviour, as time variable $t$ goes to $+\infty$, of nonautonomous gradient-like dynamical systems involving inertia and multiscale features. Given $\mathcal H$ a general Hilbert…

In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable…

In this work, the conformable Bateman Lagrangian for the damped harmonic oscillator system is proposed using the conformable derivative concept. In other words, the integer derivatives are replaced by conformable derivatives of order…

Let $X$ be an algebraic variety equipped with a dominant rational self-map $\phi:X\to X$. A new quantity measuring the interaction of $(X,\phi)$ with trivial dynamical systems is introduced; the stabilised algebraic dimension of $(X,\phi)$…

The paper analyzes a specific class of random walks on quotients of $X:=\text{SL}(k,{\Bbb R})/ \Gamma$ for a lattice $\Gamma$. Consider a one parameter diagonal subgroup, $\{g_t\}$, with an associated abelian expanding horosphere, $U\cong…

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_{\mu}=(\mu_{n,k})_{n,k\geq 0}$ with entries $\mu_{n,k}=\mu_{n+k}$, where $\mu_{n}=\int_{[0,1)}t^nd\mu(t)$, induces formally the operator as…

Let Y={f(i), Af(i),..., A^{li} f(i): i in Omega}, where A is a bounded operator on l^2(I). The problem under consideration is to find necessary and sufficient conditions on A, Omega, {l_i:i in Omega} in order to recover any f \in l^2(I)…

With a view to quantum foundations, we define the concepts of an empirical model (a probabilistic model describing measurements and outcomes), a hidden-variable model (an empirical model augmented by unobserved variables), and various…

We consider quantum systems with a Hamiltonian containing a weak perturbation i.e. $\boldsymbol{H=H_0} + \boldsymbol{\lambda} \cdot \boldsymbol{\tilde{H}}$, $\boldsymbol{\lambda}= \{\lambda_1, \lambda_2,...\}$, $\boldsymbol{\tilde{H}}$ $=…

Let $D$ be an indefinite quaternion division algebra over $\mathbb{Q}$. We approach the problem of bounding the sup-norms of automorphic forms $\phi$ on $D^\times(\mathbb{A})$ that belong to irreducible automorphic representations and…

Let $M$ be a compact $n$-dimensional Riemanian manifold, End($M$) the set of the endomorphisms of $M$ with the usual $\mathcal{C}^0$ topology and $\phi: M\to\mathbb{R}$ continuous. We prove that there exists a dense subset of $\mathcal{A}$…

In a Hilbert space $H$, in order to develop fast optimization methods, we analyze the asymptotic behavior, as time $t$ tends to infinity, of inertial continuous dynamics where the damping acts as a closed-loop control. The function $f: H…

Consider a piecewise affine Lipschitz map $\phi : \Omega \to \mathbb R$, where $\Omega \subset \mathbb R^d$ is an open set, and assume that $x \mapsto x + t \nabla \phi(x)$ is injective for almost every $t > 0$. In (J.-G. Liu, R.~L. Pego,…

We investigate in this work some situations where it is possible to estimate or determine the upper and the lower $q$-generalized fractal dimensions $D^{\pm}_{\mu}(q)$, $q\in\mathbb{R}$, of invariant measures associated with continuous…

Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its…