Related papers: Quasi-Toric Differential Inclusions
Within integrable systems, the class of so called "semitoric" integrable systems in dimension four has attracted a lot of attention in recent years, especially since fundamental examples from classical and quantum mechanics have been…
We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. This gives an interpretation for the so-called…
The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…
Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some…
Systems of differential equations with polynomial right-hand sides are very common in applications. On the other hand, their mathematical analysis is very challenging in general, due to the possibility of complex dynamics: multiple basins…
Consider a conformal map from the unit disk onto a quasidisk. We determine a range of critical complex powers with respect to which the derivative is integrable. The results fit into the picture predicted by a circular analogue of Brennan's…
In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower…
Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of…
We consider complex-balanced mass-action systems, or toric dynamical systems. They are remarkably stable polynomial dynamical systems arising from reaction networks seen as Euclidean embedded graphs. We study the moduli spaces of toric…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
We define the non-commutative multiple bi-orthogonal polynomial systems, which simultaneously generalize the concepts of multiple orthogonality, matrix orthogonal polynomials and of the bi-orthogonality. We present quasideterminantal…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian…
We consider a particular class of equations of motion, generalizing to n degrees of freedom the "dissipative spin--orbit problem", commonly studied in Celestial Mechanics. Those equations are formulated in a pseudo-Hamiltonian framework…
A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the…
A quasi-continuous dynamical system is a pair $(X,f)$ consisting of a topological space $X$ and a mapping $f: X\to X$ such that $f^n$ is quasi-continuous for all $n \in \mathbb N$, where $\mathbb N$ is the set of non-negative integers. In…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
Systems of differential equations with polynomial right-hand sides are very common in applications. In particular, when restricted to the positive orthant, they appear naturally (according to the law of mass-action kinetics) in ecology,…