Operator Structures and Dynamical Systems

Operator Structures and Dynamical Systems
Author: Marcel de Jeu
Publisher: American Mathematical Soc.
Total Pages: 329
Release: 2009-11-30
Genre: Mathematics
ISBN: 0821847473

This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008. These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included.

The Koopman Operator in Systems and Control

The Koopman Operator in Systems and Control
Author: Alexandre Mauroy
Publisher: Springer Nature
Total Pages: 568
Release: 2020-02-22
Genre: Technology & Engineering
ISBN: 3030357139

This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory. The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts: theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification; data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; and Koopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control. A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.

Differential Equations, Dynamical Systems, and Linear Algebra

Differential Equations, Dynamical Systems, and Linear Algebra
Author: Morris W. Hirsch
Publisher: Academic Press
Total Pages: 373
Release: 1974-06-28
Genre: Mathematics
ISBN: 0080873766

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

Structure of Dynamical Systems

Structure of Dynamical Systems
Author: J.M. Souriau
Publisher: Springer Science & Business Media
Total Pages: 427
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461202817

The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.

Nonlinear Dynamical Systems Of Mathematical Physics: Spectral And Symplectic Integrability Analysis

Nonlinear Dynamical Systems Of Mathematical Physics: Spectral And Symplectic Integrability Analysis
Author: Denis Blackmore
Publisher: World Scientific
Total Pages: 563
Release: 2011-03-04
Genre: Mathematics
ISBN: 9814462713

This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some innovations by the authors themselves — that have not appeared in any other book.The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained.This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.

Higher Order Networks: An Introduction to Simplicial Complexes

Higher Order Networks: An Introduction to Simplicial Complexes
Author: Ginestra Bianconi
Publisher: Cambridge University Press
Total Pages: 149
Release: 2021-12-23
Genre: Mathematics
ISBN: 1108726739

This Element presents one of the most recent developments in network science in a highly accessible style. This Element will be of interest to interdisciplinary scientists working in network science, in addition to mathematicians working in discrete topology and geometry and physicists working in quantum gravity.

Chaos in Structural Mechanics

Chaos in Structural Mechanics
Author: Jan Awrejcewicz
Publisher: Springer Science & Business Media
Total Pages: 424
Release: 2009-11-11
Genre: Technology & Engineering
ISBN: 3540776761

This volume introduces new approaches to modeling strongly nonlinear behaviour of structural mechanical units: beams, plates and shells or composite systems. The text draws on bifurcation theory and chaos, emphasizing control and stability of objects and systems.

Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology

Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology
Author: David E. Evans
Publisher: Cambridge University Press
Total Pages: 257
Release: 1988
Genre: Mathematics
ISBN: 052136843X

These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.