Related papers: On Topological Entropy of Piecewise Smooth Vector …

This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…

Perfect fluids are modeled by using an effective field theory approach which naturally gives a self-consistent and unambiguous description of the intrinsic non-adiabatic contribution to pressure variations. We study the impact of intrinsic…

Flows on surfaces are one of the most fundamental and classical objects in dynamical systems, and are studied from various areas (e.g. integrable systems, differential equations, fluid mechanics). Though hyperbolic flows and recurrent flows…

The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. In the article spherically symmetric solution of the vacuum Einstein equations in the Intuitionistic…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

Significant advancements have emerged in the theory of asymptotic stability of shear flows in stably stratified fluids. In this comprehensive review, we spotlight these recent developments, with particular emphasis on novel approaches that…

We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken…

The tensionless limit of classical string theory may be formulated as a topological theory on the world-sheet. A vector density carries geometrical information in place of an internal metric. It is found that path-integral quantization…

We construct new substantive examples of non-autonomous vector fields on 3-dimensional sphere having a simple dynamics but non-trivial topology. The construction is based on two ideas: the theory of diffeomorpisms with wild separatrix…

In this paper we study some aspects of thermodynamic formalism, more specifically topological pressure and, as a consequence, topological entropy for piecewise smooth vector fields, using topological conjugation with shift maps and the…

The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field…

Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid, incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a…

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…

In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground…

By folding nonautonomous differential systems in the plane to scalar differential equations, a sufficient condition for the non-occurrence of chaotic behavior is obtained.

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.

Relative entropy is a non-negative quantity and offers a powerful means of achieving a unified understanding of fundamental properties in physics, including the second law of thermodynamics and positivity bounds on effective field theories…

This paper is part of a series of papers on differential geometry of $C^\infty$-ringed spaces. In this paper, we study vector fields and their flows on a class of singular spaces. Our class includes arbitrary subspaces of manifolds, as well…

We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of…

In this study, we investigate the complexity of two-phase flow (air/water) in a heterogeneous soil sample by using complex network theory, where the supposed porous media is non-deformable media, under the time-dependent gas pressure. Based…