Jump to ContentJump to Main Navigation

You are looking at 1-9 of 9 items

  • Keywords: Julia set x
Clear All Modify Search

View:

Root selection and dynamical systems

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0007
Subject:
Mathematics, Probability / Statistics

This chapter explores the relationship between the numerical methods described in earlier chapters and the theory of dynamical systems. An estimating function defines a dynamical estimating system, ... More


Introducing Julia Sets

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/9780199566433.003.0023
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on the Julia set, a collection of points that do not tend toward infinity when iterated by a function. Any initial condition that is negative will become positive after one ... More


The Mandelbrot Set

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/9780199566433.003.0026
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explores whether or not Julia sets can be classified or categorised. It shows that some Julia sets are connected, forming one contiguous shape, while others are disconnected. It then ... More


Julia Sets for the Quadratic Family

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/9780199566433.003.0025
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The Julia set for a function refers to the collection of all initial conditions that do not tend toward infinity when iterated by that function. This chapter examines Julia sets that arise from ... More


Chaos and Fractals: An Elementary Introduction

David P. Feldman

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book provides an elementary introduction to chaos and fractals. It introduces the key phenomena of chaos — aperiodicity, sensitive dependence on initial conditions, bifurcations — via simple ... More


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


Dynamics on the complex plane

S. G. Rajeev

in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.003.0017
Subject:
Physics, Atomic, Laser, and Optical Physics

Iterations of an analytic function of a complex variable is a wonderful laboratory for chaos. After classifying Mobius transformations by the nature of their fixed points, this chapter turns to ... More


Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

S. G. Rajeev

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the ... More


Conclusion

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/9780199566433.003.0033
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This concluding chapter highlights some of the key themes and lessons of chaos and fractals and reflects on how their impact can be characterised. It discusses how deterministic dynamical systems can ... More


View: