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by Hans-Walter Lorenz
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Mathematics
  • Author:
    Hans-Walter Lorenz
  • ISBN:
    3540568816
  • ISBN13:
    978-3540568810
  • Genre:
  • Publisher:
    Springer; 2nd edition (February 20, 1997)
  • Pages:
    320 pages
  • Subcategory:
    Mathematics
  • Language:
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The plan to publish the present book arose while I was preparing a joint work with Gunter Gabisch (Gabisch, G. /Lorenz, H. -W. : Business Cycle Theory. Berlin-Heidel berg-New York: Springer).

The plan to publish the present book arose while I was preparing a joint work with Gunter Gabisch (Gabisch, G. It turned out that a lot of interesting material could only be sketched in a business cycle text, either because the relevance for business cycle theory was not evident or because the material required an interest in dynamical economics which laid beyond the scope of a survey text for advanced undergraduates.

334 Hans-Walter Lorenz. Nonlinear Dynamical Economics and Chaotic Motion. Springer-Verlag Berlin Heidelberg GmbH. In any case, chaotic dynamics constitute an exciting example of how complicated some dynamical systems may be, although they may at first seem to be qualitatively identical with well-known regular systems. Naturally, this book is not an essay on the purely mathematical aspects of nonlinear dynamical systems. It is designed as a survey of recent developments in dynamical systems theory and its economic applications.

Hans-Walter Lorenz  . While most examples of complex motion in economic dynamics employ a discrete-time concept, chaos can also emerge in continuous-time, nonlinear economic models

Nonlinear Dynamical Economics and Chaotic Motion. by Hans-Walter Lorenz. The book has been partly re-organized.

Nonlinear Dynamical Economics and Chaotic Motion. Select Format: Hardcover.

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Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines.

and higher-dimensional, discrete-time systems and a discussion of complex transient motion

Business Cycle Theory. and higher-dimensional, discrete-time systems and a discussion of complex transient motion. It concentrates on standard scenarios like coupled oscillator systems and forced oscillators.

Hans-Walter Lorenz, German Economist, educator. Member Royal Economics Society, American Economics Association, Econometric Society, European Economics Association. Visiting scholar, University of California-Berkeley, 1982-1983.

Usually, the first edition of a book still contains a multiplicity of typographic, con­ ceptional, and computational errors even if one believes the opposite at the time of publication. As this book did not represent a counterexample to this rule, the current second edition offers a chance to remove at least the known shortcomings. The book has been partly re-organized. The previously rather long Chapter 4 has been split into two separate chapters dealing with discrete-time and continuous­ time approaches to nonlinear economic dynamics. The short summary of basic properties of linear dynamical systems has been banned to an appendix because the line of thought in the chapter seems to have been unnecessarily interrupted by these technical details and because the book concentrates on nonlinear systems. This appendix, which mainly deals with special formal properties of dynamical sys­ tems, also contains some new material on invariant subspaces and center-manifold reductions. A brief introduction into the theory of lags and operators is followed by a few remarks on the relation between the 'true' properties of dynamical systems and their behavior observable in numerical experiments. Additional changes in the main part of the book include a re-consideration of Popper's determinism vs. inde­ terminism discussion in the light of chaotic properties of deterministic, nonlinear systems in Chapter 1. An investigation of a simultaneous price-quantity adjustment process, a more detailed inquiry into the uniqueness property of limit cycles, and a short presentation of relaxation oscillations are included in Chapter 2.