Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
Total Pages: 530
Release: 2013-04-09
Genre: Mathematics
ISBN: 1475720637

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Mathematical Physics: Classical Mechanics

Mathematical Physics: Classical Mechanics
Author: Andreas Knauf
Publisher: Springer
Total Pages: 683
Release: 2018-02-24
Genre: Science
ISBN: 3662557746

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

Modeling Complexity in Economic and Social Systems

Modeling Complexity in Economic and Social Systems
Author: Frank Schweitzer
Publisher: World Scientific
Total Pages: 408
Release: 2002
Genre: Business & Economics
ISBN: 9789812380357

Economics and the social sciences are, in fact, the ?hard? sciences, as Herbert Simon argued, because the complexity of the problems dealt with cannot simply be reduced to analytically solvable models or decomposed into separate subprocesses. Nevertheless, in recent years, the emerging interdisciplinary ?sciences of complexity? have provided new methods and tools for tackling these problems, ranging from complex data analysis to sophisticated computer simulations. In particular, advanced methods developed in the natural sciences have recently also been applied to social and economic problems.The twenty-one chapters of this book reflect this modern development from various modeling perspectives (such as agent-based models, evolutionary game theory, reinforcement learning and neural network techniques, time series analysis, non-equilibrium macroscopic dynamics) and for a broad range of socio-economic applications (market dynamics, technological evolution, spatial dynamics and economic growth, decision processes, and agent societies). They jointly demonstrate a shift of perspective in economics and the social sciences that is allowing a new outlook in this field to emerge.

Sustainable Resource Use and Economic Dynamics

Sustainable Resource Use and Economic Dynamics
Author: Lucas Bretschger
Publisher: Springer Science & Business Media
Total Pages: 235
Release: 2007-07-19
Genre: Science
ISBN: 1402062931

The chapters in the book cover a broad range of aspects regarding the relationship between natural resource use and long-term economic development. The book surveys existing literature as well as adds to frontier research. In particular, the following topics are studied: incentives for adoption and diffusion of clean technology, resource scarcity and limits to growth, international convergence of energy intensity, and the social norms shaping resource depletion.

The Elements of a Nonlinear Theory of Economic Dynamics

The Elements of a Nonlinear Theory of Economic Dynamics
Author: Carl Chiarella
Publisher: Springer Science & Business Media
Total Pages: 162
Release: 2012-12-06
Genre: Business & Economics
ISBN: 3642467075

Elements of a Nonlinear Theory of Economic Dynamics provides both a framework and a survey of its needs. First, principle results and techniques of the theory relevant to applications in dynamic economics are discussed, then their application in view of older endogenous cycle theories are considered in a unified mathematical framework. Models incorporating the government budget constraint and the Goodwin model are analysed using the method of averaging and the centre manifold theory. The dynamic instability problem is solved by placing models in a nonlinear framework.

Roy Harrod

Roy Harrod
Author: Esteban Pérez Caldentey
Publisher: Springer Nature
Total Pages: 467
Release: 2019-09-10
Genre: Business & Economics
ISBN: 1349740853

This landmark book describes and analyzes the original contributions Sir Roy Harrod made to fields including microeconomics, macroeconomics, international trade and finance, growth theory, trade cycle analysis and economic methodology. Harrod’s prolific writings reflect an astounding and unique intellectual capacity, and a wide range of interests. He became Keynes ́ biographer and wrote a volume on inductive logic. At the policy level, Harrod played a central role in the formulation of the Keynes ́ Clearing Union plan for international monetary reform. He also actively participated in British politics and government and gained recognition as an expert in the field of international economics. Yet, until now, Harrod has remained an underrated economist, commonly misunderstood and misrepresented. This is the first major intellectual biography of Harrod to be published.

The Economic Theory of Structure and Change

The Economic Theory of Structure and Change
Author: Mauro Baranzini
Publisher: CUP Archive
Total Pages: 376
Release: 1990
Genre: Business & Economics
ISBN: 9780521345163

This wide-ranging 1991 inquiry into the general field of structural economic analysis provides a thorough appraisal of the method of economic dynamics.

Economic Theory, Dynamics and Markets

Economic Theory, Dynamics and Markets
Author: Takashi Negishi
Publisher: Springer Science & Business Media
Total Pages: 542
Release: 2012-12-06
Genre: Business & Economics
ISBN: 1461516773

Economic Theory, Dynamics, and Markets. The collection of essays in honor of Ryuzo Sato, written by his colleagues and students, covers the many fields of economic theory and policy to which he has contributed. The first section pays tribute to his contributions to mathematical economics and economic theory. Ryuzo Sato is known for his work in growth theory and technical progress, and the second section has a number of papers on macroeconomics and dynamics. The third section has a number of papers on financial markets and their functioning in Japan and the United States. The next section examines various aspects of the economics of firms and industry. Ryuzo Sato has been very involved in analyzing the economic and business relations between Japan and the United States, and the last section is devoted to comparative analysis of economic systems.

Computable, Constructive & Behavioural Economic Dynamics

Computable, Constructive & Behavioural Economic Dynamics
Author: Stefano Zambelli
Publisher: Routledge
Total Pages: 812
Release: 2010-02-25
Genre: Business & Economics
ISBN: 1135272522

The book contains thirty original articles dealing with important aspects of theoretical as well as applied economic theory. While the principal focus is on: the computational and algorithmic nature of economic dynamics; individual as well as collective decision process and rational behavior, some contributions emphasize also the importance of classical recursion theory and constructive mathematics for dynamical systems, business cycles theories, growth theories, and others are in the area of history of thought, methodology and behavioural economics. The contributors range from Nobel Laureates to the promising new generation of innovative thinkers. This volume is also a Festschrift in honour of Professor Kumaraswamy Vela Velupillai, the founder of Computable Economics, a growing field of research where important results stemming from classical recursion theory and constructive mathematics are applied to economic theory. The aim and hope is to provide new tools for economic modelling. This book will be of particular appeal to postgraduate students and scholars in one or more of the following fields: computable economics, business cycles, macroeconomics, growth theories, methodology, behavioural economics, financial economics, experimental and agent based economics. It might be also of importance to those interested on the general theme of algorithmic foundations for social sciences.