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Chaos, Fractals and Dynamical Systems

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Lecture 39: The Monodromy Matrix and the Saltation Matrix

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Lecture Series on Chaos, Fractals and Dynamical Systems by Prof.S.Banerjee,Department of Electrical Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in.

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Lecture Series on Chaos, Fractals and Dynamical Systems by Prof.S.Banerjee,Department of Electrical Engineering, IIT Kharagpur.

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  1. Lecture - 1 Representations of Dynamical Systems
  2. Lecture - 2 Vector Fields of Nonlinear Systems
  3. Lecture - 3 Limit Cycles
  4. Lecture - 4 The Lorenz Equation - I
  5. Lecture - 5 The Lorenz Equation - II
  6. Lecture - 6 The Rossler Equation and Forced Pendulum
  7. Lecture - 7 The Chua's Circuit
  8. Lecture - 8 Discrete Time Dynamical Systems
  9. Lecture - 9 The Logistic Map and Period doubling
  10. Lecture - 10 Flip and Tangent Bifurcations
  11. Lecture - 11 Intermittency Transcritical and pitchfork
  12. Lecture - 12 Two Dimensional Maps
  13. Lecture - 13 Bifurcations in Two Dimensional Maps
  14. Lecture - 14 Introduction to Fractals
  15. Lecture - 15 Mandelbrot Sets and Julia Sets
  16. Lecture - 16 The Space Where Fractals Live
  17. Lecture - 17 Interactive Function Systems
  18. Lecture - 18 IFS Algorithms
  19. Lecture - 19 Fractal Image Compression
  20. Lecture - 20 Stable and Unstable Manifolds
  21. Lecture - 21 Boundary Crisis and Interior Crisis
  22. Lecture - 22 Statistics of Chaotic Attractors
  23. Lecture - 23 Matrix Times Circle : Ellipse
  24. Lecture - 24 Lyapunov Exponent
  25. Lecture - 25 Frequency Spectra of Orbits
  26. Lecture - 26 Dynamics on a Torus
  27. Lecture - 27 Dynamics on a Torus
  28. Lecture - 28 Analysis of Chaotic Time Series
  29. Lecture - 29 Analysis of Chaotic Time Series
  30. Lecture - 30 Lyapunou Function and Centre Manifold Theory
  31. Lecture - 31 Non-Smooth Bifurcations
  32. Lecture - 32 Non-Smooth Bifurcations
  33. Lecture - 33 Normal from for Piecewise Smooth 2D Maps
  34. Lecture - 34 Bifurcations in Piecewise Linear 2D Maps
  35. Lecture - 35 Bifurcations in Piecewise Linear 2D Maps
  36. Lecture - 36 Multiple Attractor Bifurcation and Dangerous
  37. Lecture - 37 Dynamics of Discontinuous Maps
  38. Lecture - 38 Introduction to Floquet Theory
  39. Lecture - 39 The Monodromy Matrix and the Saltation Matrix
  40. Lecture - 40 Control of Chaos