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Cornell MAE 5790: Nonlinear Dynamics and Chaos →0/22
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MAE5790-1 Course introduction and overview

1:16:31
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MAE5790-2 One dimensional Systems

1:16:44
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MAE5790-3 Overdamped bead on a rotating hoop

1:13:12
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MAE5790-4 Model of an insect outbreak

1:15:16
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MAE5790-5 Two dimensional linear systems

1:15:20
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MAE5790-6 Two dimensional nonlinear systems fixed points

1:07:17
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MAE5790-7 Conservative Systems

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MAE5790-8 Index theory and introduction to limit cycles

1:13:55
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Lecture 9: Testing for Closed Orbits (MAE 5790)

1:16:52
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Lecture 10: Van der Pol Oscillator (MAE 5790)

1:05:58
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Lecture 11: Averaging Theory for Weakly Nonlinear Oscillators (MAE 5790)

1:16:08
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Lecture 12: Bifurcations in Two-Dimensional Systems (MAE 5790)

46:54
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Lecture 13: Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators (MAE 5790)

1:07:57
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Lecture 14: Global Bifurcations of Cycles (MAE 5790)

1:16:23
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Lecture 15: Chaotic Waterwheel (MAE 5790)

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Lecture 16: Waterwheel Equations and Lorenz Equations (MAE 5790)

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Lecture 17: Chaos in the Lorenz Equations (MAE 5790)

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Lecture 18: Strange Attractor for the Lorenz Equations (MAE 5790)

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Lecture 19: One-Dimensional Maps (MAE 5790)

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Lecture 20: Universal Aspects of Period Doubling (MAE 5790)

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Lecture 21: Feigenbaum's Renormalization Analysis of Period Doubling (MAE 5790)

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Lecture 22: Renormalization: Function Space and a Hands-On Calculation (MAE 5790)

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Lecture 22: Renormalization: Function Space and a Hands-On Calculation (MAE 5790)

Steven StrogatzCornell University

Professor

1:08:32·2014·undergraduate level

This lecture introduces the concept of an infinite-dimensional function space, where the renormalization transformation acts as a mapping. It identifies the universal function 'g' as a saddle point and the scaling factor delta as an unstable eigenvalue, demonstrating a concrete renormalization calculation.

MathematicsEngineeringControl & Dynamical SystemsLinear AlgebraRenormalization GroupFunction Space

The concept of an infinite-dimensional space of functions. Each point represents a function. Renormalization transformation T as a mapping. Sheets of functions with the same superstability type. The universal function g as a saddle point of T. The scaling factor delta is the unstable eigenvalue of DT. Concrete renormalization, using only high school algebra, gives alpha and delta to within about 10 percent.

Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 10.7.

Previous · Lecture 21

Lecture 21: Feigenbaum's Renormalization Analysis of Period Doubling (MAE 5790)

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