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Maximal Tori in Infinite-Dimensional Hamiltonian Systems: a Renormalisation Group Approach
We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each...
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On some pre-orders and partial orders of linear operators on infinite dimensional vector spaces
This article is devoted to the generalization of the Drazin pre-order and the G-Drazin partial order to Core-Nilpotent endomorphisms over arbitrary k -...
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The Chain Control Set of Discrete-Time Linear Systems on the Affine Two-Dimensional Lie Group
In this paper, we present conditions for the existence and uniqueness of chain control sets of discrete-time linear systems on the affine...
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Some Infinite-Dimensional Geometric Examples
In this chapter, we discuss several examples illustrating the nature of infinite-dimensional algebro-geometric objects for which the constructions...
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Explicit Solutions of Infinite Linear Systems Associated with Group Inverse Endomorphisms
The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As...
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Infinite Dimensional Control
The study of infinite dimensional optimal control has been a rapidly growing area of research (Ahmed, Comm Appl Nonlinear Anal 16:1-14, 2009; Ahmed,...
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Some Infinite-Dimensional Representations of Certain Coxeter Groups
A Coxeter group admits infinite-dimensional irreducible complex representations if and only if it is not finite or affine. In this paper, we provide...
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On the Michor–Mumford phenomenon in the infinite dimensional Heisenberg group
In the infinite dimensional Heisenberg group, we construct a left invariant weak Riemannian metric that gives a degenerate geodesic distance. The...
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Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions
We prove Cameron-Martin type quasi-invariance for the heat kernel measure of infinite-dimensional Kolmogorov and similar degenerate diffusions. We...
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Application of Banach limits to invariant measures of infinite-dimensional Hamiltonian flows
Applying an invariant measure on phase space, we study the Koopman representation of a group of symplectomorphisms in an infinite-dimensional Hilbert...
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Topological and Homological Properties of the Orbit Space of a Simple Three-Dimensional Compact Linear Lie Group
AbstractThe question of whether an orbit space of a compact linear group is a topological manifold and a homology manifold is studied. The case of...
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Solvability of an Infinite System of Linear Algebraic Equations with an Infinite Number of Unknowns
AbstractA new theory of solvability of linear equations with an infinite number of unknowns has been developed.
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On Some Properties of the Shift on an Infinite-Dimensional Torus
AbstractWe study the question, classical in the theory of dynamical systems, about the minimality of the shift on an infinite-dimensional torus;...
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Convergence to Infinite-Dimensional Compound Poisson Distributions on Convex Polyhedra
The present work is aimed at supplementing the authors’ paper (2018). Our results on the approximation of distributions of sums of independent...
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Infinite Dimensional Control
The study of infinite dimensional optimal control has been a rapidly growing area of research. In this chapter we present preliminaries which we need...
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On Infinite-dimensional Lie Algebra of Navier–Stokes Equation and Conservation Laws
The primary focus of this article is to study (2+1)-dimensional Navier–Stokes equation for Lie point symmetries and local conservation laws. The...
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Finite Dimensional Group Representations
Algebraic relations among matrices, if any, are encapsulated in their characteristic polynomial. How to decipher this information thus becomes an...
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The \(C^*\) -Algebra of the Infinite Dihedral Group \(D_{\infty }\)
The infinite dihedral group \(D_{\infty }=\langle a, t\mid a^2=t^2=1\rangle \)...
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Infinite-Dimensional Stochastic Hamiltonian Systems
The infinite-dimensional stochastic Hamiltonian systems arise in various fields such as stochastic electromagnetics, quantum physics and stochastic...
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Conditional and Hidden Infinite-Dimensional Symmetries of Wave Equations
We consider conditional and hidden symmetries of multidimensional wave equations generated by additional conditions. An additional condition...