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Quantifying Chaos

Robert C. Hilborn

in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507239
eISBN:
9780191709340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507239.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explores various means of quantifying the degree of chaotic behaviour of both numerically generated time series and time series from real experiments. These methods include Lyapunov ... More


Classical Analysis

John Stillwell

in Reverse Mathematics: Proofs from the Inside Out

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691196411
eISBN:
9781400889037
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691196411.003.0003
Subject:
Mathematics, History of Mathematics

This chapter explores the basic concepts that arise when real numbers and continuous functions are studied, particularly the limit concept and its use in proving properties of continuous functions. ... More


Capitalism as Creative, Chaotic Evolution by Structural Change

Richard M. Goodwin

in Chaotic Economic Dynamics

Published in print:
1990
Published Online:
November 2003
ISBN:
9780198283355
eISBN:
9780191596315
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283350.003.0001
Subject:
Economics and Finance, Macro- and Monetary Economics

As in meteorology, prediction in economics is hampered by highly irregular, chaotic dynamics. A two‐sector model is employed to examine the complementary growth theories of Schumpeter and Keynes ... More


Dimensions

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0017
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explains how to characterise fractals by means of the dimension. It defines dimension in terms of the scaling properties of a shape in order to describe fractals quantitatively. The ... More


Ends of Groups

Nic Koban and John Meier

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0010
Subject:
Mathematics, Geometry / Topology

This chapter focuses on the ends of a group. It first constructs a group action on the Cantor set and creates a free group from bijections of the Cantor set before showing how the idea of trying to ... More


Introducing Fractals

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on fractals and the role of iteration in their generation. It first considers three familiar shapes from geometry: a circle, a line segment, and a rectangle. It then describes a ... More


Henry Smith

Keith Hannabuss

in Oxford Figures: Eight Centuries of the Mathematical Sciences

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199681976
eISBN:
9780191761737
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199681976.003.0012
Subject:
Mathematics, History of Mathematics

Henry Smith was the first substantial mathematician to occupy the Savilian Chair of Geometry for well over a century. A highly cultured man who spoke several languages, he made internationally ... More


The Box‐Counting Dimension

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0019
Subject:
Physics, Theoretical, Computational, and Statistical Physics

There are several examples of fractals that are not exactly self-similar, as is the case with small parts of the random Koch curve which exhibit statistical self-similarity but not identicality. The ... More


Spatial Scale and Species Diversity: Building Species–Area Curves from Species Incidence

Jack J. Lennon and William Edward Kunin

in Biodiversity in Drylands: Toward a Unified Framework

Published in print:
2005
Published Online:
November 2020
ISBN:
9780195139853
eISBN:
9780197561720
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195139853.003.0011
Subject:
Earth Sciences and Geography, Environmental Geography

This chapter is largely focused on the species–area relationship (SAR), although it may not seem so for much of the time. Bear with us; we will get there ... More


Unifying Laws in Multidisciplinary Power-Law Phenomena: Fixed-Point Universality and Nonextensive Entropy

Alberto Robledo

in Nonextensive Entropy: Interdisciplinary Applications

Published in print:
2004
Published Online:
November 2020
ISBN:
9780195159769
eISBN:
9780197562024
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195159769.003.0008
Subject:
Earth Sciences and Geography, Atmospheric Sciences

Critical, power-law behavior in space and/or time manifests in a large variety of complex systems [12] within physics and, nowadays, more conspicuously in other ... More


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