عنوان

Dynamics with chaos and fractals /

شابک

3030358542

شابک

9783030358549

شابک اشتباه

3030358534

شابک اشتباه

9783030358532

عنوان اصلي

Dynamics with chaos and fractals /

نام عام مواد

[Book]

نام نخستين پديدآور

Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily.

محل نشرو پخش و غیره

Cham :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2020.

نام خاص و کميت اثر

1 online resource (233 pages)

عنوان فروست

Nonlinear Systems and Complexity ;

مشخصه جلد

v. 29

متن يادداشت

11.5 Dynamics Motivated by Sierpinski Fractals

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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

بدون عنوان

0

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

متن يادداشت

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.

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783030358549

عنوان

Dynamics with Chaos and Fractals.

شماره استاندارد بين المللي کتاب و موسيقي

9783030358532

موضوع مستند نشده

Chaotic behavior in systems.

موضوع مستند نشده

Fractals.

موضوع مستند نشده

Chaotic behavior in systems.

موضوع مستند نشده

Fractals.

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Akhmet, Marat.

مستند نام اشخاص تاييد نشده

Alejaily, Ejaily Milad.

مستند نام اشخاص تاييد نشده

Fen, Mehmet Onur.

تاريخ عمليات

20200823094601.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y