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\n4.0 A better way to understand Differential Equations | Nonlinear Dynamics | Index Theory\n

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\nIndex theory is a method used to gain global information about a nonlinear differential equation. One powerful insight is that closed orbits (periodic solutions) must have at least one fixed point inside of the curve. In fact, for a...\nIndex theory is a method used to gain global information about a nonlinear differential equation. One powerful insight is that closed orbits (periodic solutions) must have at least one fixed point inside of the curve. In fact, for a periodic orbit, there must be 1 more fixed point of index = +1 than saddle fixed points.Chapters: 0:00 Last time 0:48 Intro 0:58 Motivation 2:04 Index of Closed Orbits 3:53 Index Examples 6:02 Defining Phi and Index 8:18 Proof Index Integer 8:47 Proof Index Constant Under Deformation 10:24 Index of Fixed Points 10:49 Index of Multiple Fixed Points 12:38 Index Closed Orbits = +1 13:00 Examples Closed Orbits 13:53 Ruling Out Closed Orbits 14:13 Next time 14:32 Outro\n
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Resource Details

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Educator Rating
Not yet Rated
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Media Length
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14:34
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Grade
Higher Ed
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Subjects
Math
7 more...
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Media Type
Instructional Videos
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Source:
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\nVirtually Passed\n\n
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Date
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2022
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Language
English
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Audiences
For Teacher Use
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Usage Permissions
Fine Print: Educational Use
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Concepts

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series, index, questions, trajectory, differential equations, eigenvalues
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nonlinear equations, index theory, chaos, periodic solutions, limit cycles, closed orbit, nonlinear dynamics, vector field, upper part, net change, fixed point, closed curve, net index, integer, change, saddle, indices, point, answer, curve, call, case, minus, arrow, talked, particle, understand, video, begin, question, started
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