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An Introduction to Dynamical Systems and Chaos de G. C. Layek

An Introduction to Dynamical Systems and Chaos: University Texts in the Mathematical Sciences

Autor G. C. Layek
en Limba Engleză Paperback – 23 feb 2025

Bazându-ne pe datele furnizate de editura Springer și pe structura riguroasă a seriei University Texts in the Mathematical Sciences, remarcăm că această a doua ediție (2024) a lucrării An Introduction to Dynamical Systems and Chaos reprezintă o resursă fundamentală, actualizată pentru cerințele actuale ale programelor de studiu în matematică și inginerie. Subliniem organizarea secvențială a materialului, care facilitează o tranziție logică de la fluxurile unidimensionale la complexitatea sistemelor neliniare. Primele opt capitole sunt dedicate sistemelor continue, unde descoperim un accent deosebit pus pe analiza stabilității și teoria bifurcațiilor. Un element de noutate și distincție față de manualele introductive standard este capitolul dedicat analizei de simetrie, unde G. C. Layek introduce principiul invarianței Lie, tratând simetria ca o caracteristică intrinsecă a sistemelor neliniare.

În a doua parte a volumului, atenția se mută către sistemele discrete, explorând haosul și fractalii prin prisma relațiilor de conjugare și a proprietăților hărților matematice. Comparabil cu Nonlinear Systems de P. G. Drazin în ceea ce privește rigurozitatea tratării oscilațiilor și echilibrului, lucrarea de față se diferențiază prin actualizarea conținutului pentru a include progresele recente din ultimele decenii și prin adăugarea unui capitol final dedicat turbulenței, de la Reynolds la Kolmogorov. Structura pedagogică este consolidată de numeroase exemple lucrate detaliat și exerciții plasate la finalul capitolelor, transformând teoria abstractă într-un instrument de lucru aplicat pentru modelarea fenomenelor complexe.

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Specificații

ISBN-13: 9789819976973
ISBN-10: 9819976979
Pagini: 708
Dimensiuni: 155 x 235 x 36 mm
Greutate: 1.18 kg
Ediția:Second Edition 2024
Editura: Springer
Colecția University Texts in the Mathematical Sciences
Seria University Texts in the Mathematical Sciences

De ce să citești această carte

Recomandăm acest volum studenților de la facultățile de matematică, fizică și inginerie care doresc o înțelegere profundă a dinamicii neliniare. Cititorul câștigă nu doar o bază teoretică solidă, ci și competențe practice prin studiul bifurcațiilor și al sistemelor hamiltoniene. Este o resursă esențială pentru cei care urmăresc să aplice teoria haosului în cercetare, oferind un echilibru rar între formalismul matematic și claritatea expunerii.

Despre autor

G. C. Layek este un cadru didactic și cercetător recunoscut, cu o expertiză vastă în domeniul matematicii aplicate. Contribuția sa în cadrul seriei University Texts in the Mathematical Sciences de la Springer reflectă o preocupare constantă pentru sistematizarea conceptelor complexe din dinamica sistemelor. Autorul pune un accent deosebit pe integrarea metodelor analitice, precum analiza de simetrie Lie, în studiul fenomenelor de haos și turbulență, facilitând accesul studenților la instrumente matematice avansate utilizate în cercetarea modernă.

Descriere

This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable coexisting attractors.

Cuprins

1. Continuous Dynamical Systems.- 2. Linear Systems.- 3. Phase Plane Analysis.- 4. Stability Theory.- 5. Oscillation.- 6. Theory of Bifurcations.- 7. Hamiltonian Systems.- 8. Symmetry Analysis.- 9. Discrete Dynamical Systems.- 10. Some maps.- 11. Conjugacy Maps.- 12. Chaos.- 13. Fractals.- 14. Turbulence: Reynolds to Kolmogrov and Beyond.- Index.

Recenzii

“The text is a strong and rigorous treatment of the introduction of dynamical systems … . The exercises presented at the end of each chapter are suitable for upper-level undergraduates and graduate students. As a reference source, the text is very well-organized with its division of the subject into continuous and discrete dynamical systems. Summing Up: Recommended. Upper-division undergraduates through professionals and practitioners.” (M. D. Sanford, Choice, Vol. 54 (2), October, 2016)
This textbook provides a clear presentation of many standard topics in dynamical systems. Overall, the book is well written in a clear logical manner. The chapter titles precisely indicate the topics covered by the author. These are…..  
 
s="" are="" used="" in="" study="" of="" continuous="" discrete="" dynamical="" systems.="" due="" to="" combination="" a="" careful="" development="" theory,="" many="" worked="" example="" problems,="" variety="" applications,="" well-chosen="" exercises, An introduction to dynamical systems and chaos is very well suited as either a course text or for self-study by students. The book could also serve as a nice supplement to many of the other standard texts on dynamical systems.

Notă biografică

G. C. LAYEK is a Professor of the Department of Mathematics, The University of Burdwan, India. He received his Ph.D. degree from Indian Institute of Technology, Kharagpur and did his Post doctoral studies at Indian Statistical Institute, Kolkata. His areas of research are nonlinear dynamics, chaos theory, turbulence, boundary layer flows and thermal sciences. Professor Layek has published more than 100 research papers in international journals of repute. He taught more than two decades at the post-graduate level in the University of Burdwan. He made several international academic visits, such asLaboratoire de Me ́canique des Fluides de Lille (LMFL), Centrale Lille, France as ‘Professeur invitaé’, Saint Petersburg State University and Kazan State Technological University, Russia for collaborative research works. Layek and Pati’s model (Physics Letters A, 381: 3568-3575, 2017) got recognition for exploring bifurcations and Shil’nikov chaos in Rayleigh-Bénard convection of a Boussinesq fluid layer heated underneath taking non-Fourier heat-flux. The existence of non-Kolmogorov turbulence is established for free-shear turbulent flows, viz., turbulent wake, jet and thermal plume flows through Lie symmetry analysis on statistical turbulent model equations. He has made significant contributions for identification of organized structures in transitional routes and chaotic regimes of many physical phenomena.He now focuses research works on organized structures in chaos and turbulence.

Textul de pe ultima copertă

The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonianflows and symmetries of nonlinear systems are among the main focuses of this book.
 
Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.

Caracteristici

Presents a comprehensive overview of nonlinear dynamics Discusses continuous and discrete systems by using a systematic, sequential, and logical approach Presents numerous solved examples with physical explanations of oscillations, bifurcations, and Lie symmetry analysis of nonlinear systems Explains conjugacy, chaos, and fractals in detail Is useful to students of mathematics, physics, and engineering Includes supplementary material: sn.pub/extras