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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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