An Introduction to Dynamical Systems and Chaos

ISBN-13: 9789819976942 / Angielski

G. C. Layek

Spis treści

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. 

O autorze

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.

Blurb

This 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 several examples are worked out in detail and exercises have been included. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate and graduate students in mathematics, physics, and engineering. 

The second edition of the book includes a new chapter on Reynold and Kolmogrov turbulence. The entire book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillation, pitchfork bifurcation, transcritical bifurcation, Bogdonov–Takens bifurcation, canonical invariant and symmetry properties, turbulent planar plume flow, and dynamics on circle, organized structure in chaos and multifractals.