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Simplicial Dynamical Systems
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Book Synopsis Simplicial Dynamical Systems by : Ethan Akin
Download or read book Simplicial Dynamical Systems written by Ethan Akin and published by American Mathematical Soc.. This book was released on 1999 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: A simplicial dynamical system is a simplicial map $g: K DEGREES* \rightarrow K$ where $K$ is a finite simplicial complex triangulating a compact polyhedron $X$ and $K DEGREES*$ is a proper subdivision of $K$, for example, the barycentric or any further subdivision. the dynamics of the asociated piecewise linear map $g: X X$ can be analyzed by using certain naturally related subshifts of finite type. Any continous map on $X$ can be $C DEGREES0$ approximated by such systems. Other examples yield interesting
Book Synopsis Simplicial Dynamical Systems by : Ethan Akin
Download or read book Simplicial Dynamical Systems written by Ethan Akin and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: A simplicial dynamical system is a simplicial map $g: K DEGREES* \rightarrow K$ where $K$ is a finite simplicial complex triangulating a compact polyhedron $X$ and $K DEGREES*$ is a proper subdivision of $K$, for example, the barycentric or any further subdivision. the dynamics of the asociated piecewise linear map $g: X X$ can be analyzed by using certain naturally related subshifts of finite type. Any continous map on $X$ can be $C DEGREES0$ approximated by such systems. Other examples yield interesting
Book Synopsis Introduction to the Modern Theory of Dynamical Systems by : Anatole Katok
Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
Book Synopsis Simplicial Complexes In Complex Systems: In Search For Alternatives by : Yi Zhao
Download or read book Simplicial Complexes In Complex Systems: In Search For Alternatives written by Yi Zhao and published by World Scientific. This book was released on 2021-05-25 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the last few decades researchers from different fields gather their findings and knowledge trying to give a shape to the new science of complex systems. To address this problem, new tools and methods have to be established. A new, or more precisely an alternative, framework for the characterization of complex system was proposed. In this book we will introduce the applicability of applicability of simplicial complexes in the science of complex systems. After introducing the main definitions and properties of simplicial complexes necessary for representation and analysis of complex systems, we will illustrate the usefulness and versatility of tools and concepts related to the simplicial complexes.
Book Synopsis Control of Uncertain Dynamic Systems by : Shankar P. Bhattacharyya
Download or read book Control of Uncertain Dynamic Systems written by Shankar P. Bhattacharyya and published by CRC Press. This book was released on 2020-09-23 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of 34 papers presented by leading researchers at the International Workshop on Robust Control held in San Antonio, Texas in March 1991. The common theme tying these papers together is the analysis, synthesis, and design of control systems subject to various uncertainties. The papers describe the latest results in parametric understanding, H8 uncertainty, l1 optical control, and Quantitative Feedback Theory (QFT). The book is the first to bring together all the diverse points of view addressing the robust control problem and should strongly influence development in the robust control field for years to come. For this reason, control theorists, engineers, and applied mathematicians should consider it a crucial acquisition for their libraries.
Author :Krzysztof R. Kozlowski Publisher :Springer Science & Business Media ISBN 13 :1848829841 Total Pages :490 pages Book Rating :4.8/5 (488 download)
Book Synopsis Robot Motion and Control 2009 by : Krzysztof R. Kozlowski
Download or read book Robot Motion and Control 2009 written by Krzysztof R. Kozlowski and published by Springer Science & Business Media. This book was released on 2009-11-15 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robot Motion Control 2009 presents very recent results in robot motion and control. Forty short papers have been chosen from those presented at the sixth International Workshop on Robot Motion and Control held in Poland in June 2009. The authors of these papers have been carefully selected and represent leading institutions in this field. The following recent developments are discussed: design of trajectory planning schemes for holonomic and nonholonomic systems with optimization of energy, torque limitations and other factors, new control algorithms for industrial robots, nonholonomic systems and legged robots, different applications of robotic systems in industry and everyday life, like medicine, education, entertainment and others, multiagent systems consisting of mobile and flying robots with their applications. The book is suitable for graduate students of automation and robotics, informatics and management, mechatronics, electronics and production engineering systems as well as scientists and researchers working in these fields.
Book Synopsis Higher-Order Systems by : Federico Battiston
Download or read book Higher-Order Systems written by Federico Battiston and published by Springer Nature. This book was released on 2022-04-26 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the potential of higher-order interactions to model real-world relational systems. Over the last decade, networks have emerged as the paradigmatic framework to model complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited to pairwise interactions, limiting our ability to describe, understand, and predict complex phenomena which arise from higher-order interactions. Here we introduce the new modeling framework of higher-order systems, where hypergraphs and simplicial complexes are used to describe complex patterns of interactions among any number of agents. This book is intended both as a first introduction and an overview of the state of the art of this rapidly emerging field, serving as a reference for network scientists interested in better modeling the interconnected world we live in.
Book Synopsis Topological Dimension and Dynamical Systems by : Michel Coornaert
Download or read book Topological Dimension and Dynamical Systems written by Michel Coornaert and published by Springer. This book was released on 2015-06-20 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner’s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored.
Book Synopsis The Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems by : Basil Nicolaenko
Download or read book The Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems written by Basil Nicolaenko and published by American Mathematical Soc.. This book was released on 1989 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold-that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.
Book Synopsis Computational Models of Complex Systems by : Vijay Kumar Mago
Download or read book Computational Models of Complex Systems written by Vijay Kumar Mago and published by Springer Science & Business Media. This book was released on 2013-10-31 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational and mathematical models provide us with the opportunities to investigate the complexities of real world problems. They allow us to apply our best analytical methods to define problems in a clearly mathematical manner and exhaustively test our solutions before committing expensive resources. This is made possible by assuming parameter(s) in a bounded environment, allowing for controllable experimentation, not always possible in live scenarios. For example, simulation of computational models allows the testing of theories in a manner that is both fundamentally deductive and experimental in nature. The main ingredients for such research ideas come from multiple disciplines and the importance of interdisciplinary research is well recognized by the scientific community. This book provides a window to the novel endeavours of the research communities to present their works by highlighting the value of computational modelling as a research tool when investigating complex systems. We hope that the readers will have stimulating experiences to pursue research in these directions.
Book Synopsis Dynamical Numbers: Interplay between Dynamical Systems and Number Theory by : S. F. Koli︠a︡da
Download or read book Dynamical Numbers: Interplay between Dynamical Systems and Number Theory written by S. F. Koli︠a︡da and published by American Mathematical Soc.. This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers from the special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic dynamical systems.
Book Synopsis Higher Order Networks: An Introduction to Simplicial Complexes by : Ginestra Bianconi
Download or read book Higher Order Networks: An Introduction to Simplicial Complexes written by Ginestra Bianconi and published by Cambridge University Press. This book was released on 2021-12-23 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamics of Topologically Generic Homeomorphisms by : Ethan Akin
Download or read book Dynamics of Topologically Generic Homeomorphisms written by Ethan Akin and published by American Mathematical Soc.. This book was released on 2003 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this work is to describe the dynamics of generic homeomorphisms of certain compact metric spaces $X$. Here ``generic'' is used in the topological sense -- a property of homeomorphisms on $X$ is generic if the set of homeomorphisms with the property contains a residual subset (in the sense of Baire category) of the space of all homeomorphisms on $X$. The spaces $X$ we consider are those with enough local homogeneity to allow certain localized perturbations of homeomorphisms; for example, any compact manifold is such a space. We show that the dynamics of a generic homeomorphism is quite complicated, with a number of distinct dynamical behaviors coexisting (some resemble subshifts of finite type, others, which we call `generalized adding machines', appear strictly periodic when viewed to any finite precision, but are not actually periodic). Such a homeomorphism has infinitely many, intricately nested attractors and repellors, and uncountably many distinct dynamically-connected components of the chain recurrent set. We single out several types of these ``chain components'', and show that each type occurs densely (in an appropriate sense) in the chain recurrent set. We also identify one type that occurs generically in the chain recurrent set. We also show that, at least for $X$ a manifold, the chain recurrent set of a generic homeomorphism is a Cantor set, so its complement is open and dense. Somewhat surprisingly, there is a residual subset of $X$ consisting of points whose limit sets are chain components of a type other than the type of chain components that are residual in the space of all chain components. In fact, for each generic homeomorphism on $X$ there is a residual subset of points of $X$ satisfying a stability condition stronger than Lyapunov stability.
Book Synopsis Emerging Frontiers in Nonlinear Science by : Panayotis G. Kevrekidis
Download or read book Emerging Frontiers in Nonlinear Science written by Panayotis G. Kevrekidis and published by Springer Nature. This book was released on 2020-05-29 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead. This interdisciplinary book presents contributions from a diverse group of experts from various fields to provide an overview of each field’s past, present and future. It will appeal to both beginners and seasoned researchers in nonlinear science, numerous areas of physics (optics, quantum physics, biophysics), and applied mathematics (ODEs, PDEs, dynamical systems, machine learning) as well as engineering.
Book Synopsis Computer Algebra in Scientific Computing by : V.G. Ganzha
Download or read book Computer Algebra in Scientific Computing written by V.G. Ganzha and published by Springer. This book was released on 2007-09-04 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Workshop on Computer Algebra in Scientific Computing, CASC 2007, held in Bonn, Germany, in September 2007. The volume is dedicated to Professor Vladimir P. Gerdt on the occasion of his 60th birthday. The papers cover not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms.
Book Synopsis Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion by : Alexander Fel'shtyn
Download or read book Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion written by Alexander Fel'shtyn and published by American Mathematical Soc.. This book was released on 2000 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.
Book Synopsis New Trends in Differential Equations, Control Theory and Optimization by : Viorel Barbu
Download or read book New Trends in Differential Equations, Control Theory and Optimization written by Viorel Barbu and published by World Scientific. This book was released on 2016-06-17 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains a collection of original papers and surveys in various areas of Differential Equations, Control Theory and Optimization written by well-known specialists and is thus useful for PhD students and researchers in applied mathematics. Contents:Dirichlet Problems with Mean Curvature Operator in Minkowski Space (Cristian Bereanu, Petru Jebelean and Călin Şerban)Free Boundary Fluid-Elasticity Interactions: Adjoint Sensitivity Analysis (Lorena Bociu and Kristina Martin)Non-Smooth Regularization of a Forward-Backward Parabolic Equation (Elena Bonetti, Pierluigi Colli and Giuseppe Tomassetti)Approaching Monotone Inclusion Problems via Second Order Dynamical Systems with Linear and Anisotropic Damping (Radu Ioan Boţ and Ernö Robert Csetnek)On the Solutions of a Quadratic Integral Inclusion (Aurelian Cernea)On the Bounded and Stabilizing Solution of a Generalized Riccati Differential Equation with Periodic Coefficients Arising in Connection with a Zero Sum Linear Quadratic Stochastic Differential Game (Vasile Dragan and Toader Morozan)A Maximum Principle for a Class of First Order Differential Operators (Maria Fărcăşeanu, Mihai Mihăilescu and Denisa Stancu-Dumitru)Differentiability and Integrability Properties for Solutions to Nonlocal Equations (Mikil Foss and Petronela Radu)Ferroelectric Thin Structures (Antonio Gaudiello and Kamel Hamdache)Sliding Modes for a Phase-Field System (Gianni Gilardi)Uniformly Hyperbolic Viable Sets in Affine IFS (Vasile Glavan and Valeriu Guţu)Some Support Considerations in the Asymptotic Optimality of Two-Scale Controlled PDMP (Dan Goreac and Oana Silvia Serea)Inverse Problems for Control Theory (Mohammed Al Horani and Angelo Favini)On the Ill-Posedness of Active Scalar Equations with Odd Singular Kernels (Igor Kukavica, Vlad Vicol and Fei Wang)Equilibrium in an Individual — Societal SIR Vaccination Model in Presence of Discounting and Finite Vaccination Capacity (Laetitia Laguzet, Gabriel Turinici and Ghozlane Yahiaoui)On Some Minimization Problems in RN (Mihai Mariş)Recent Results on Multiple Periodic Solutions of Forced Relativistic Pendulum-Type Continuous and Discrete Systems (Jean Mawhin)On the Anisotropic Caginalp Phase-Field System with Singular Nonlinear Terms (Alain Miranville)Space, Time, Similarity (Umberto Mosco)Singularly Perturbed Problems for Abstract Differential Equations of Second Order in Hilbert Spaces (Andrei Perjan and Galina Rusu)Global Controllability and Mixing for the Burgers Equation with Localised Finite-Dimensional External Force (Armen Shirikyan)Boundary Observation in Shape Optimization (Dan Tiba)Recent Progress on Steady Gravity Water Waves (Eugen Vărvărucă) Readership: Researchers in partial differential equations, calculus of variations and optimal control, difference and functional equations.
