Related papers: Genericity on submanifolds and application to Univ…

Let $\{a_t: t \in \mathbb{R}\}< SL_{d}(\mathbb{R})$ be a diagonalizable subgroup whose expanding horospherical subgroup $U < SL_{d}(\mathbb{R})$ is abelian. By the Birkhoff ergodic theorem, for any $x \in…

In this paper we prove results on Birkhoff and Oseledets genericity along certain curves in the space of affine lattices and in moduli spaces of translation surfaces. We also prove applications of these results to dynamical billiards,…

We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every…

We consider ergodic multiflows on a probability space. The general theorem on universal averaging for multiflows is applied to averaging along manifolds in $R^n$.

The notions of (metric) hypersurface data were introduced in [Mars,2013] as a tool to analyze, from an abstract viewpoint, hypersurfaces of arbitrary signature in pseudo-riemannian manifolds. In this paper, general geometric properties of…

We introduce a general notion of "genericity" for countable subsets of a space with Borel measure, and apply it to the set of vertices in the curve complex of a surface S, interpreted as subset of the space of projective measured…

We investigate generic properties (i.e. properties corresponding to residual sets) in the space of subshifts with the Hausdorff metric. Our results deal with four spaces: the space $\mathbf{S}$ of all subshifts, the space…

The classical theorem of Birkhoff states that the $T^N f(x) = (1/N)\sum_{k=0}^{N-1} f(\sigma^k x)$ converges almost everywhere for $x\in X$ and $f\in L^{1}(X)$, where $\sigma$ is a measure preserving transformation of a probability measure…

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 $M$ be a closed and connected manifold, $H:T^*M\times \mathbb{R} / \mathbb{Z} \to \mathbb{R}$ a Tonelli $1$-periodic Hamiltonian and $\mathcal{L} \subset T^*M$ a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We…

The Birkhoff Ergodic Theorem concludes that time averages, that is, Birkhoff averages, $\Sigma_{n=1}^N f(x_n)/N$ of a function $f$ along an ergodic trajectory $(x_n)$ of a function $T$ converges to the space average $\int f d\mu$, where…

We prove that the Birkhoff pointwise ergodic theorem and the Oseledets multiplicative ergodic theorem hold for every flat surface in almost every direction. The proofs rely on the strong law of large numbers, and on recent rigidity results…

The Birkhoff Ergodic Theorem concludes that time averages, i.e., Birkhoff averages, $\Sigma_{n=0}^{N-1} f(x_n)/N$ of a function $f$ along a length $N$ ergodic trajectory $(x_n)$ of a function $T$ converge to the space average $\int f d\mu$,…

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White, we…

In this work we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one may calculate the mean hitting time for a particle to reach a chosen goal subspace. The questions…

We explore the sum over topologies in AdS$_3$ quantum gravity and its relationship with the statistical interpretation of the boundary theory. We formulate a statistical version of the conformal bootstrap that systematizes the universal…

We study the class of transversal submanifolds. We characterize their blow-ups at transversal points and prove a negligibility theorem for their "generalized characteristic set", with respect to the Carnot-Carath\'eodory Hausdorff measure.…

We use subsequence and moving average ergodic theorems applied to Boole's transformation and its variants and their invariant measures on the real line to give new characterisations of the Lindelh{\"o}f Hypothesis and the Riemann…

The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This…

In this paper we mainly study the dynamical complexity of Birkhoff ergodic average under the simultaneous observation of any number of continuous functions. These results can be as generalizations of [6,35] etc. to study Birkhorff ergodic…