me961outline2006 - Outline ME961 Fall 2006 1 Analysis of...

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Outline: ME961 Fall 2006 1. Analysis of Mathematical Models (ordinary differential equations and maps) flows and maps (GH 1.2,1.4; W 0; NB 1.1-1.2; S 2, 10) linearizations (GH 1.1-1.4; W 1.1A; NB 2.1,2.2; S 2.4, 5, 6.3) hyperbolicity, invariant subspaces, Hartman-Grobman theorem invariant manifolds (GH 1.6; W 1.1C; NB 2.1.3) asymptotic behavior (GH 1.6; W 1.1H; NB 1.3; S 9.3) Poincare maps (GH 1.5; W 1.2; NB 7.6; S 8.7) structural stability (GH 1.7; W 1.2C; NB 2.3.7; S 6.3) center manifolds (GH 3.2; W 2.1; NB 2.3.4) local bifurcations (GH 3.1, 3.4, 3.5; W 3; NB 2.3; S 3, 8) normal forms (GH 3.3; W 2.2) averaging (GH 4.1-4.3; W 1.2D) Melnikov method (GH 4.5-4.6; W 4.5; NB 5.7) 2. Symbol Dynamics 1-D and 2-D maps: (GH 5.0-5.6; W 4.1-4.3) horseshoe map, chaotic sets, Cantor set. 3. Routes to chaos (papers also provided as refs.) period doubling (GH 6.1; NB, BPV 8) intermittency (GH 6.1; NB, BPV 9) qusiperiodic routes to chaos (GH 6.1, NB, BPV 7) examples References (should be on reserve at the Engineering Library)
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This note was uploaded on 03/15/2010 for the course ME 961 taught by Professor Staff during the Spring '08 term at Michigan State University.

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me961outline2006 - Outline ME961 Fall 2006 1 Analysis of...

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