Advanced Fixed Point Theory for Economics

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Sprache: Englisch

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Beschreibung

This book develops the central aspect of fixed point theory ¿ the topological fixed point index ¿ to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems.

The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs.

Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstandingtext for advanced graduate courses in economics and related disciplines.

Über den Autor

Andrew McLennan received his PhD from Princeton in 1982 under the supervision of Hugo Sonnenschein, and is currently Professor at the University of Queensland School of Economics. His primary research interests are in game theory, mathematical economics and microeconomics.

Zusammenfassung

Provides comprehensive coverage of fixed point theory at the highest possible level of generality

Avoids use of algebraic topology, resulting in intuitive and geometric arguments as well as greater accessibility

Requires no mathematical knowledge beyond that which is common to all theoretical economists

Inhaltsverzeichnis

Chapter 1 Introduction and Summary.- Part I Topological Methods.- Chapter 2 Planes, Polyhedra, and Polytopes.- Chapter 3 Computing Fixed Points.- Chapter 4 Topologies on Spaces of Sets.- Chapter 5 Topologies on Functions and Correspondences.- Chapter 6 Metric Space Theory.- Chapter 7 Retracts.- Chapter 8 Essential Sets of Fixed Points.- Chapter 9 Approximation of Correspondences.- Part II Smooth Methods.- Chapter 10 Differentiable Manifolds.- Chapter 11 Sard's Theorem.- Chapter 12 Degree Theory.- Chapter 13 The Fixed Point Index.- Part III Applications and Extensions.- Chapter 14 Topological Consequences.- Chapter 15 Vector Fields and their Equilibria.

Details

Erscheinungsjahr:	2018
Fachbereich:	Volkswirtschaft
Genre:	Importe , Wirtschaft
Rubrik:	Recht & Wirtschaft
Medium:	Buch
Inhalt:	xx 432 S. 18 s/w Illustr. 432 p. 18 illus.
ISBN-13:	9789811307096
ISBN-10:	9811307091
Sprache:	Englisch
Herstellernummer:	978-981-13-0709-6
Einband:	Gebunden
Autor:	McLennan, Andrew
Auflage:	1st edition 2018
Hersteller:	Springer Singapore Springer Nature Singapore
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 30 mm
Von/Mit:	Andrew McLennan
Erscheinungsdatum:	20.07.2018
Gewicht:	0,84 kg