Optical Vortices : Fundamentals and Applications.

Format:

Book

Author/Creator:

Yang, Yuanjie.

Contributor:

Ren, Yuxuan.

Rosales-Guzmán, Carmelo.

Series:

IOP Ebooks Series

Language:

English

Subjects (All):

Optical vortices.

Photonics.

Physical Description:

1 online resource (356 pages)

Edition:

1st ed.

Place of Publication:

Bristol : Institute of Physics Publishing, 2024.

Summary:

This book focus on the latest advances in optical vortices field, from fundamentals to applications. The goal of this book is to present the optical vortices to a broad audience.

Contents:

Outline placeholder

References

Author biography

Marat Akhmet

Chapter Historical and philosophical overview

1.1 Outline

1.2 A new mathematical structure

1.3 Alpha labels in spiraled hierarchy of mathematical structures

1.4 Universality and minimalism of alpha labeling and unpredictability

1.5 Principle of excessiveness: the Universe approximates science

1.6 Potential and actual uncertainty in dynamics

1.7 Actual uncertainty of chaos

1.8 Monads spiral up to abstract similarity

1.9 Alpha labeling for more chaos and fractals

1.10 Ancient Greek chaos

1.11 Alpha unpredictability and alpha labeling decrease formalism of chaos

1.12 Mathematical chaos and H. Poincaré

1.13 Alpha unpredictability versus sensitivity

1.14 Ultra Poincaré chaos versus Li-Yorke chaos

1.15 Chaos as a metaphor

1.16 Does the theory of chaos exist?

1.17 Ubiquitous chaos and dualism

1.18 Domain of chaos

Chapter Alpha labels are a new mathematical structure

2.1 Sets of alpha labels and alpha map

2.1.1 Alpha sets and rectangles

2.1.2 Alpha maps and self-similarity

2.2 Alpha dynamics

2.2.1 Algorithm of alpha labeling for dynamical systems

2.2.2 How to apply alpha dynamics

2.2.3 Alpha dynamics versus symbolic dynamics

2.3 Alpha chaos

2.3.1 Basic conditions for alpha chaos

2.3.2 Theorems by alpha dynamics

2.4 Examples of alpha chaotic models

2.4.1 Symbolic dynamics

2.4.2 Alpha chaos in finite sets

2.4.3 Cantor middle set

2.4.4 Multi-folded Baker map

2.4.5 The logistic map

2.5 Hyperbolic alpha labeling

2.5.1 Hyperbolic alpha dynamics

2.5.2 Abstract hyperbolic chaos

2.5.3 Alpha hyperbolic chaos

2.5.4 Examples of alpha hyperbolic chaos

2.6 Modular chaos

2.6.1 Introduction

2.6.2 Modular chaos in alpha dynamics.

2.6.3 Modular chaos through alpha labeling

2.6.4 Examples of modular chaos

2.7 Abstract fractals: alpha spaces with measures

2.7.1 Abstract fractals as alpha induced sets

2.7.2 Alpha fractals in 2D geometry

2.8 Notes

Chapter Alpha unpredictability implies a universal mathematical chaos

3.1 Poincaré and Lorenz lines in a nutshell

3.2 An individual chaos: alpha unpredictability

3.3 Alpha unpredictable functions: appearance of chaos

3.4 Notes

Chapter Compartmental alpha unpredictable functions

4.1 Continuous compartmental unpredictable functions

4.1.1 Kappa property of unbounded sequences

4.1.2 Alpha unpredictability of compartmental periodic functions

4.1.3 Alpha unpredictable functions related to the logistic equation

4.1.4 Degree of periodicity and numerical simulations

4.1.5 Randomly determined compartmental unpredictable functions

4.2 Discontinuous compartmental periodic Poisson stable functions

4.2.1 Poisson sequences

4.2.2 Compartmental functions

4.2.3 Examples with numerical simulations

4.3 Algebra and significance for applications

4.4 Notes

Chapter Alpha unpredictable differential equations

5.1 Strongly alpha unpredictable solutions

5.1.1 Definitions and auxiliaries

5.1.2 The existence theorem

5.1.3 Alpha unpredictable solutions

5.1.4 Examples with numerical simulations

5.2 Compartmental quasi-linear equations

5.2.1 Definitions and auxiliaries

5.2.2 The existence theorem

5.2.3 Examples with numerical simulations

5.3 Modulo periodic Poisson stable solutions

5.3.1 Preliminaries

5.3.2 A linear non-homogeneous system

5.3.3 Examples with numerical simulations

5.3.4 A quasi-linear system

5.3.5 Modulo periodic Poisson stable coefficients

5.4 Notes

References.

Chapter Ultra Poincaré chaos numerically

6.1 Introduction and preliminaries

6.2 The algorithm of the test and the application procedure

6.3 Ultra Poincaré chaos for revisited models

6.3.1 Devaney's chaos subdued to the sequential test

6.3.2 Considering Li-Yorke chaos

6.3.3 Explaining results of bifurcation diagrams analysis

6.3.4 Rössler System analyzed by its Lyapunov exponents

6.3.5 Ikeda map with positive Lyapunov exponents

6.3.6 Intermittency through the ultra Poincaré test

6.4 Alpha unpredictability test is positive for known strange non-chaotic attractors

6.4.1 Introduction and preliminaries

6.4.2 A continuous-time model

6.4.3 A discrete-time model

6.5 The generalized synchronization as a proof of alpha unpredictability

6.5.1 Introduction and preliminaries

6.5.2 Ultra Poincaré chaos of the response system

6.5.3 An example with numerical simulations

6.6 Notes

Chapter Alpha labeled randomness

7.1 Alpha unpredictability in Bernoulli schemes

7.2 Alpha unpredictable functions randomly

7.3 Alpha unpredictable strings and statistical laws

7.3.1 Basic dynamics of strings

7.3.2 Laws of large strings

7.4 Modular chaos in random processes

7.4.1 Chaos and randomness

7.4.2 Modular chaotic random processes

7.4.3 Examples with numerical simulations

7.4.4 Notes

Chapter Markov chains and stochastic differential equations

8.1 Alpha chaos in Markov chains

8.1.1 Markov chains with alpha dynamics

8.1.2 An example: random walk

8.2 Duffing type equations with Markov coefficients

8.2.1 Elements of alpha unpredictable functions

8.2.2 Markovian coefficients

8.2.3 Random processes

8.2.4 A numerical example and discussions

8.3 Notes

Chapter Alpha induced dynamics in fractals and cubes.

9.1 Historical observations

9.2 Alpha induced dynamics in metric spaces

9.2.1 Alpha labels and alpha map

9.2.2 Alpha induced dynamics

9.2.3 How to make chaotic geometry

9.3 Chaotic cubes

9.3.1 Chaotic line segment

9.3.2 Chaotic square and 3D cube

9.3.3 Chaos in multidimensional cubes

9.4 Alpha chaos in Fatou-Julia iterations

9.4.1 Logistic maps with alpha chaos

9.4.2 Perturbed logistic systems

9.5 Notes

Notes:

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Other Format:

Print version: Yang, Yuanjie Optical Vortices

ISBN:

9780750358446

OCLC:

1472148582