Invariant Sets for Windows

Invariant Sets for Windows

Author: Albert D. Morozov

Publisher: World Scientific

Published: 1999

Total Pages: 280

ISBN-13: 9789810240714

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This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 96 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book. The book consists of two parts. Part I contains a description of WlnSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical systems to computer design. In Part II, the invariant sets presented in Part I are investigated from the theoretical perspective. The invariant sets of dynamical systems with one, one-and-a-half and two degrees of freedom, as well as those of two-dimensional maps, are discussed. The basic models of the diffusion equations are also considered. This part of the book is intended for a more advanced reader, with at least a BSc in Mathematics.


Red Kant: Aesthetics, Marxism and the Third Critique

Red Kant: Aesthetics, Marxism and the Third Critique

Author: Michael Wayne

Publisher: Bloomsbury Publishing

Published: 2014-09-25

Total Pages: 237

ISBN-13: 1472508688

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Is Kant really the 'bourgeois' philosopher that his advocates and opponents take him to be? In this bold and original re-thinking of Kant, Michael Wayne argues that with his aesthetic turn in the Third Critique, Kant broke significantly from the problematic philosophical structure of the Critique of Pure Reason. Through his philosophy of the aesthetic Kant begins to circumnavigate the dualities in his thought. In so doing he shows us today how the aesthetic is a powerful means for imagining our way past the apparent universality of contemporary capitalism. Here is an unfamiliar Kant: his concepts of beauty and the sublime are reinterpreted as attempts to socialise the aesthetic while Wayne reconstructs the usually hidden genealogy between Kant and important Marxist concepts such as totality, dialectics, mediation and even production. In materialising Kant's philosophy, this book simultaneously offers a Marxist defence of creativity and imagination grounded in our power to think metaphorically and in Kant's concept of reflective judgment. Wayne also critiques aspects of Marxist cultural theory that have not accorded the aesthetic the relative autonomy and specificity which it is due. Discussing such thinkers as Adorno, Bourdieu, Colletti, Eagleton, Lukács, Ranciére and others, Red Kant: Aesthetics, Marxism and the Third Critique presents a new reading of Kant's Third Critique that challenges Marxist and mainstream assessments of Kant alike.


Transient Chaos

Transient Chaos

Author: Ying-Cheng Lai

Publisher: Springer Science & Business Media

Published: 2011-02-26

Total Pages: 499

ISBN-13: 144196987X

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The aim of this Book is to give an overview, based on the results of nearly three decades of intensive research, of transient chaos. One belief that motivates us to write this book is that, transient chaos may not have been appreciated even within the nonlinear-science community, let alone other scientific disciplines.


Fixed Point Theory and Best Approximation: The KKM-map Principle

Fixed Point Theory and Best Approximation: The KKM-map Principle

Author: S.P. Singh

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 231

ISBN-13: 9401588228

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The aim of this volume is to make available to a large audience recent material in nonlinear functional analysis that has not been covered in book format before. Here, several topics of current and growing interest are systematically presented, such as fixed point theory, best approximation, the KKM-map principle, and results related to optimization theory, variational inequalities and complementarity problems. Illustrations of suitable applications are given, the links between results in various fields of research are highlighted, and an up-to-date bibliography is included to assist readers in further studies. Audience: This book will be of interest to graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations and expansions, convex sets and related geometric topics and game theory.


Hierarchical Nonlinear Switching Control Design with Applications to Propulsion Systems

Hierarchical Nonlinear Switching Control Design with Applications to Propulsion Systems

Author: Alexander Leonessa

Publisher: Springer Science & Business Media

Published: 2000-07-17

Total Pages: 156

ISBN-13: 9781852333355

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This book presents a general nonlinear control design methodology for nonlinear uncertain dynamical systems. Specifically, a hierarchical nonlinear switching control framework is developed that provides a rigorous alternative to gain scheduling control for general nonlinear uncertain systems. The proposed switching control design framework accounts for actuator saturation constraints as well as system modeling uncertainty. The efficacy of the control design approach is extensively demonstrated on aeroengine propulsion systems. In particular, dynamic models for rotating stall and surge in axial and centrifugal flow compression systems that lend themselves to the application of nonlinear control design are developed and the hierarchical switching control framework is then applied to control the aerodynamic instabilities of rotating stall and surge. For the researcher who is entering the field of hierarchical switching robust control this book provides a plethora of new research directions. Alternatively, for researchers already active in the field of hierarchical control and hybrid systems, this book can be used as a reference to a significant body of recent work. Furthermore, control practitioners involved with nonlinear control design can immensely benefit from the novel nonlinear stabilization techniques presented in the book.


Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures

Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures

Author: Viktor Avrutin

Publisher: World Scientific

Published: 2019-05-28

Total Pages: 649

ISBN-13: 9811204713

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The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.


Differentiable and Complex Dynamics of Several Variables

Differentiable and Complex Dynamics of Several Variables

Author: Pei-Chu Hu

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 348

ISBN-13: 9401592993

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The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.


Computer Algebra in Scientific Computing

Computer Algebra in Scientific Computing

Author: Vladimir P. Gerdt

Publisher: Springer

Published: 2009-09-30

Total Pages: 402

ISBN-13: 3642041035

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This book constitutes the refereed proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing, CASC 2009, held in Kobe, Japan, in September 2009. The 28 revised full papers presented together with 2 invited lectures were carefully reviewed and selected from numerous submissions. The topics addressed are all basic areas of scientific computing as they benefit from the application of computer algebra methods and software. The papers cover computer algebra methods and algorithms, application of symbolic and algebraic manipulation, and CA methods and results for the numerical integration of the partial differential equations of the mathematical physics.


Elementary Symbolic Dynamics And Chaos In Dissipative Systems

Elementary Symbolic Dynamics And Chaos In Dissipative Systems

Author: Bailin Hao

Publisher: World Scientific

Published: 1989-09-01

Total Pages: 478

ISBN-13: 9814520012

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This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical rigour. The author used elementary mathematics and calculus, and relied on physical intuition whenever possible. Substantial attention is paid to numerical techniques in the study of chaos. Part of the book is based on the publications of Chinese researchers, including those of the author's collaborators.


Simulating, Analyzing, and Animating Dynamical Systems

Simulating, Analyzing, and Animating Dynamical Systems

Author: Bard Ermentrout

Publisher: SIAM

Published: 2002-01-01

Total Pages: 304

ISBN-13: 9780898718195

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Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modeling techniques and methods for analyzing the resulting equations.