Calendar

Calendar table.
LEC #	TOPICS	KEY DATES
1	Introduction
2	*Lecture by Prof. Thomas Peacock* Pendulum Free Oscillator Global View of Dynamics Energy in the Plane Pendulum
3	Lecture by Prof. Thomas Peacock Stability of Solutions to ODEs Linear Systems Nonlinear Systems Conservation of Volume in Phase Space	Problem set 1 due
4	Damped Oscillators and Dissipative Systems General Remarks Phase Portrait of Damped Pendulum Summary Forced Oscillators and Limit Cycles General Remarks Van der Pol Equation Energy Balance for Small ε Limit Cycle for ε Large A Final Note
5	Parametric Oscillator Mathieu Equation Elements of Floquet Theory Stability of the Parametric Pendulum Damping Further Physical Insight	Problem set 2 due
6	Fourier Transforms Continuous Fourier Transform Discrete Fourier Transform Inverse DFT Autocorrelations, Power Spectra, and the Wiener-Khinitchine Theorem
7	Fourier Transforms (cont.) Power Spectrum of a Periodic Signal - Sinusoidal Signal - Non-sinusoidal Signal - t_max/T ≠ Integer - Conclusion	Problem set 3 due
8	Fourier Transforms (cont.) Quasiperiodic Signals Aperiodic Signals Poincaré Sections Construction of Poincaré Sections
9	Poincaré Sections (cont.) Types of Poincaré Sections - Periodic - Quasiperiodic Flows - Aperiodic Flows First-return Maps 1-D Flows Relation of Flows to Maps - Example 1: The Van der Pol Equation
10	Poincaré Sections (cont.) Relation of Flows to Maps (cont.) - Example 2: Rössler Attractor - Example 3: Reconstruction of Phase Space from Experimental Data Fluid Dynamics and Rayleigh-Bénard Convection The Concept of a Continuum Mass Conservation	Problem set 4 due
11	Fluid Dynamics and Rayleigh Bénard Convection (cont.) Momentum Conservation - Substantial Derivative - Forces on Fluid Particle Nondimensionalization of Navier-Stokes Equations Rayleigh-Bénard Convection
12	Fluid Dynamics and Rayleigh-Bénard Convection (cont.) Rayleigh-Bénard Equations - Dimensional Form - Dimensionless Equations - Bifurcation Diagram - Pattern Formation - Convection in the Earth	Problem set 5 due
13	Midterm Exam
14	Introduction to Strange Attractors Dissipation and Attraction Attractors with d = 2 Aperiodic Attractors Example: Rössler Attractor Conclusion
15	Lorenz Equations Physical Problem and Parametrization Equations of Motion - Momentum Equation - Temperature Equation Dimensionless Equations	Problem set 6 due
16	Lorenz Equations (cont.) Stability Dissipation Numerical Equations Conclusion
17	Hénon Attractor The Hénon Map Dissipation Numerical Simulations Experimental Attractors Rayleigh-Bénard Convection Belousov-Zhabotinsky Reaction Fractals Definition
18	Fractals (cont.) Examples Correlation Dimention ν - Definition - Computation Relationship of ν to D	Problem set 7 due
19	Lyaponov Exponents Diverging Trajectories Example 1: M Independent of Time Example 2: Time-dependent Eigenvalues Numerical Evaluation Lyaponov Exponents and Attractors in 3-D Smale's Horseshoe Attractor
20	Period Doubling Route to Chaos Instability of a Limit Cycle Logistic Map Fixed Points and Stability
21	Period Doubling Route to Chaos (cont.) Period Doubling Bifurcations Scaling and Universality	Problem set 8 due
22	Period Doubling Route to Chaos Universal Limit of Iterated Rescaled ƒ's Doubling Operator Computation of α
23	Period Doubling Route to Chaos (cont.) Linearized Doubling Operator Computation of δ Comparison to Experiments	Problem set 9 due
24	Guest lecture by Prof. Edward N. Lorenz
25	Intermittency (and Quasiperiodicity) General Characteristics of Intermittency One-dimensional Map Average Duration of Laminar Phase Lyaponov Number
26	Intermittency (and Quasiperiodicity) (cont.) Quasiperiodicity Special Topic	Final problem set due

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