عنوان

Dynamics with chaos and fractals /

(Number (ISBN

3030358542

(Number (ISBN

9783030358549

Erroneous ISBN

3030358534

Erroneous ISBN

9783030358532

Title Proper

Dynamics with chaos and fractals /

General Material Designation

[Book]

First Statement of Responsibility

Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily.

Place of Publication, Distribution, etc.

Cham :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2020.

Specific Material Designation and Extent of Item

1 online resource (233 pages)

Series Title

Nonlinear Systems and Complexity ;

Volume Designation

v. 29

Text of Note

11.5 Dynamics Motivated by Sierpinski Fractals

Text of Note

Includes bibliographical references and index.

Text of Note

Intro -- Preface -- Contents -- 1 Introduction -- References -- 2 The Unpredictable Point and Poincaré Chaos -- 2.1 Preliminaries -- 2.2 Dynamics with Unpredictable Points -- 2.3 Chaos on the Quasi-Minimal Set -- 2.4 Applications -- 2.5 Notes -- References -- 3 Unpredictability in Bebutov Dynamics -- 3.1 Introduction -- 3.2 Preliminaries -- 3.3 Unpredictable Functions -- 3.4 Unpredictable Solutions of Quasilinear Systems -- 3.5 Examples -- 3.6 Notes -- References -- 4 Nonlinear Unpredictable Perturbations -- 4.1 Preliminaries -- 4.2 An Unpredictable Sequence of the Symbolic Dynamics

Text of Note

10 Global Weather and Climate in the Light of El Niño-Southern Oscillation -- 10.1 Introduction and Preliminaries -- 10.1.1 Unpredictability of Weather and Deterministic Chaos -- 10.1.2 Ocean-Atmosphere Interaction and Its Effects on Global Weather -- 10.1.3 El Niño Chaotic Dynamics -- 10.1.4 Sea Surface Temperature Advection Equation -- 10.1.5 Unpredictability and Poincaré Chaos -- 10.1.6 The Role of Chaos in Global Weather and Climate -- 10.2 Unpredictable Solution of the Advection Equation -- 10.2.1 Unpredictability Due to the Forcing Source Term

Text of Note

10.2.2 Unpredictability Due to the Current Velocity -- 10.3 Chaotic Dynamics of the Global Ocean Parameters -- 10.3.1 Extension of Chaos in Coupled Advection Equations -- 10.3.2 Coupling of the Advection Equation with VallisModel -- 10.3.3 Coupling of Vallis Models -- 10.4 Ocean-Atmosphere Unpredictability Interaction -- 10.5 Notes -- References -- 11 Fractals: Dynamics in the Geometry -- 11.1 Introduction -- 11.2 Fatou-Julia Iteration -- 11.3 How to Map Fractals -- 11.4 Dynamics for Julia Sets -- 11.4.1 Discrete Dynamics -- 11.4.2 Continuous Dynamics

Text of Note

4.3 An Unpredictable Solution of the Logistic Map -- 4.4 An Unpredictable Function -- 4.5 Unpredictable Solutions of Differential Equations -- 4.6 Notes -- References -- 5 Unpredictability in Topological Dynamics -- 5.1 Introduction -- 5.2 Quasilinear Delay Differential Equations -- 5.3 Quasilinear Discrete Equations -- 5.4 A Continuous Unpredictable Function via the Logistic Map -- 5.5 Examples -- 5.6 A Hopfield Neural Network -- 5.7 Notes -- References -- 6 Unpredictable Solutions of Hyperbolic Linear Equations -- 6.1 Preliminaries -- 6.2 Differential Equations with Unpredictable Solutions

Text of Note

6.3 Discrete Equations with Unpredictable Solutions -- 6.4 Examples -- References -- 7 Strongly Unpredictable Solutions -- 7.1 Preliminaries -- 7.2 Main Results -- 7.3 Examples -- References -- 8 Li-Yorke Chaos in Hybrid Systems on a Time Scale -- 8.1 Introduction -- 8.2 Preliminaries -- 8.3 Bounded Solutions -- 8.4 The Chaotic Dynamics -- 8.5 An Example -- 8.6 Notes -- References -- 9 Homoclinic and Heteroclinic Motions in Economic Models -- 9.1 Introduction -- 9.2 The Model -- 9.3 Homoclinic and Heteroclinic Motions -- 9.4 An Example -- 9.5 Notes -- References

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Text of Note

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested. The Book Stands as the first book presenting theoretical background on the unpredictable point and mapping of fractals Introduces the concepts of unpredictable functions, abstract self-similarity, and similarity map Discusses unpredictable solutions of quasilinear ordinary and functional differential equations Illustrates new ways to construct fractals based on the ideas of Fatou and Julia Examines unpredictability in ocean dynamics and neural networks, chaos in hybrid systems on a time scale, and homoclinic and heteroclinic motions in economic models.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030358549

Title

Dynamics with Chaos and Fractals.

International Standard Book Number

9783030358532

Chaotic behavior in systems.

Fractals.

Chaotic behavior in systems.

Fractals.

Number

Edition

Class number

Akhmet, Marat.

Alejaily, Ejaily Milad.

Fen, Mehmet Onur.

Date of Transaction

20200823094601.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y