Related papers: Double variational principle for mean dimension wi…
We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can…
Motivated by various applications and examples, the standard notion of potential for dynamical systems has been generalized to almost additive and asymptotically additive potential sequences, and the corresponding thermodynamic formalism,…
We introduce the mean Assouad dimension of a dynamical system, motivated by the Assouad dimension in fractal geometry. Using dimension interpolation, we further define the mean Assouad spectrum. This provides a new family of bi-Lipschitz…
Let $(X,d,f)$ be a topological dynamical system, where $(X,d)$ is a compact metric space and $f:X\to X$ is a continuous map. We define $n$-ordered empirical measure of $x\in X$ by \begin{align*}…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributions. We give a constructive proof of the existence of minimal…
We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
A simultaneous variational principle is introduced that offers a novel avenue to the description of the equilibrium configurations, and at the same time of the elementary excitations, or undulations, of fluid lipid membranes, described by a…
Fundamental duality is a concept which refers to two irreducible, heterogeneous principles which are in opposite and complementary of each other. The complementary principle in quantum mechanics is also praised by Bohr. This important…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other similar spaces of probability measures into locally compact…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
We add a random bulk term, modelling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double well potential. We show that in $d\le2$…
Tsukamoto (2022) introduced the notion of Bedford-McMullen carpet system, a subsystem of $([0,1]^{\mathbb{N}}\times[0,1]^{\mathbb{N}},shift)$ whose metric mean dimension and mean Hausdorff dimension does not coincide in general. The aim of…
A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…