相关论文: On the shortest distance between orbits and the lo…

We consider rapidly mixing dynamical systems and link the decay of the shortest distance between multiple orbits with the generalized fractal dimension. We apply this result to multidimensional expanding maps and extend it to the realm of…

We study the minimal distance between two orbit segments of length n, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random…

We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…

In this paper, we investigate the asymptotic behavior of the shortest distance between observed orbits in two distinct dynamical systems. Given two measure-preserving transformations $(X, T, \mu)$ and $(X, S, \eta)$ and a Lipschitz…

The shortest distance between the first $n$ iterates of a typical point can be quantified with a log rule for some dynamical systems admitting Gibbs measures. We show this in two settings. For topologically mixing Markov shifts with at most…

We continue our investigation of the phenomenological implications of the "deformed" commutation relations [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. These commutation relations are motivated by the fact that they lead to…

Given a dynamical system, we prove that the shortest distance between two $n$-orbits scales like $n$ to a power even when the system has slow mixing properties, thus building and improving on results of Barros, Liao and the first author. We…

In this paper, we discuss the role of the shortest distance in time-dependent enclosure method for the inverse problems when the inclusions are embedded in a non-layered or two-layered medium. Furthermore, the regularity assumptions for the…

Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…

Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions…

Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…

Exchange interaction strongly influences the long-range behaviour of localised electron orbitals. It violates the oscillation theorem (creates extra nodes) and produces a power-law decay instead of the usual exponential decrease at large…

In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…

Consider the action of a connected complex reductive group on a finite-dimensional vector space. A fundamental result in invariant theory states that the orbit closure of a vector v is separated from the origin if and only if some…

The increasing congestion in the near-Earth space environment has amplified the need for robust and efficient conjunction analysis techniques including the computation of the minimum distance between orbital paths in the presence of…

In the pattern formation problem, robots in a system must self-coordinate to form a given pattern, regardless of translation, rotation, uniform-scaling, and/or reflection. In other words, a valid final configuration of the system is a…

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two…

The computation of the Minimum Orbital Intersection Distance (MOID) is an old, but increasingly relevant problem. Fast and precise methods for MOID computation are needed to select potentially hazardous asteroids from a large catalogue. The…

We consider the minimal distance between orbits of measure preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which almost sure asymptotic closeness properties can be ensured.…

We study the approximation hardness of the Shortest Superstring, the Maximal Compression and the Maximum Asymmetric Traveling Salesperson (MAX-ATSP) problem. We introduce a new reduction method that produces strongly restricted instances of…