12.006J / 18.353J Nonlinear Dynamics I: Chaos, Fall 2005

Rothman, Daniel H.

Author(s)

Rothman, Daniel H.

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Alternative title

Nonlinear Dynamics I: Chaos

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Abstract

Introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. Forced and parametric oscillators. Phase space. Periodic, quasiperiodic, and aperiodic flows. Sensitivity to initial conditions and strange attractors. Lorenz attractor. Period doubling, intermittency, and quasiperiodicity. Scaling and universality. Analysis of experimental data: Fourier transforms, Poincar, sections, fractal dimension, and Lyapunov exponents. Applications drawn from fluid dynamics, physics, geophysics, and chemistry. See 12.207J/18.354J for Nonlinear Dynamics II.

Date issued

2005-12

URI

http://hdl.handle.net/1721.1/38877

Department

Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences; Massachusetts Institute of Technology. Department of Mathematics

Other identifiers

12.006J-Fall2005

local: 12.006J

local: 18.353J

local: IMSCP-MD5-569427a72390c1f0fe7d4609b4ed7a72

Keywords

Forced and parametric oscillators, Phase space, Periodic, quasiperiodic, and aperiodic flows, Sensitivity to initial conditions and strange attractors, Lorenz attractor, Period doubling, intermittency, and quasiperiodicity, Scaling and universality, Analysis of experimental data: Fourier transforms, Poincaré sections, fractal dimension, Lyaponov exponents

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