18.385j/2.036j MIT
Hopf Bifurcations.
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, Massachusetts MA 02139
Abstract
In two dimensions a Hopf bifurcation occurs as a Spiral Point switches from stable
to unstable (or vice versa)
Bead moving along a thin, rigid, wire.
Rodolfo R. Rosales,
Department of Mathematics,
Massachusetts Inst. of Technology, Cambridge, Massachusetts, MA 02139
October 17, 2004
Abstract
An equation describing the motion of a b ead along a rigid wire is derive
Bifurcations: baby normal forms.
Rodolfo R. Rosales,
Department of Mathematics,
Massachusetts Inst. of Technology, Cambridge, Massachusetts, MA 02139
October 10, 2004
Abstract
The normal forms for the various bifurcations that can o ccur in a one dimensio
18.385j/2.036j, MIT
Weakly Nonlinear Things: Oscillators.
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, Massachusetts MA 02139
Abstract
When nonlinearities are small there are various ways one can exploit this
fact and the fac
18.385j/2.036j, MIT.
Tricky Asymptotics Fixed Point Notes.
Contents
1 Introduction.
2
2 Qualitative analysis.
2
3 Quantitative analysis, and failure for n = 2.
6
4 Resolution of the diculty in the case n = 2.
9
5 Exact solution of the orbit equation.
14
6
MIT 18.385j/2.036j
First Problem Set
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Suggested Readings (textbook): Chapters 1-2-3.
Suggested Problems (textbook):
Ch. 2: 2.2.9
2.2.12 2.2.13 2.3.3
2.4.9
2.6.1
2.8.3
2.8.5
Ch. 3: 3.3.1
3.4.5
3.4.7
3.4.8
3.4.9
3.4.10
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Problems to hand in for grading (te