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We prove several topological and dynamical properties of the boundary of a hierarchically hyperbolic group are independent of the specific hierarchically hyperbolic structure. This is accomplished by proving that the boundary is invariant…
We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.
We give a means for measuring the equation of evolution of a complex scalar field that is known to obey an otherwise unspecified (2+1)-dimensional dissipative nonlinear parabolic differential equation, given field moduli over three…
The conjugacy classes of so-called special involutions parameterize the constituents of the action of a finite Coxeter group on the cohomology of the complement of its complexified hyperplane arrangement. In this note we give a short…
We consider the matrix representation of the Eisenstein numbers and in this context we discuss the theory of the Pseudo Hyperbolic Functions. We develop a geometrical interpretation and show the usefulness of the method in Physical problems…
This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of…
A boundary value problem related to a parabolic higher order operator with a small parameter is analized. When the small parameter tends to zero, the reduced operator is hyperbolic. When t tends to infinity a parabolic hyperbolic boundary…
The space forms, the complex hyperbolic spaces and the quaternionic hyperbolic spaces are characterized as the harmonic manifolds with specific radial eigenfunctions of the Laplacian.
The methods are proposed for evaluation of complex dynamical systems, choice of their optimal operating modes, determination of optimal operating system from given class of equivalent systems, system's timeline behaviour analysis on the…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from…
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…
We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian…
In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably,…
Functions of hyperbolic type encode representations on real or complex hyperbolic spaces, usually infinite-dimensional. These notes set up the complex case. As applications, we prove the existence of a non-trivial deformation family of…
This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new way. Our…
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in…
Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…