The Topology of Chaos - Department of Physics - Drexel University

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Chaos The Topology of Chaos Robert Gilmore Intro.-01 Intro.-02 Intro.-03 Exp’tal-01 Exp’tal-02 Exp’tal-03 Exp’tal-04 Exp’tal-05 Exp’tal-06 Exp’tal-07 Motion that is • Deterministic: • Recurrent • Non Periodic Chaos dx dt = f(x) • Sensitive to Initial Conditions Exp’tal-08 Embed-01 Embed-02 Embed-03
Strange Attractor The Topology of Chaos Robert Gilmore Intro.-01 Intro.-02 Intro.-03 Exp’tal-01 Exp’tal-02 Exp’tal-03 Exp’tal-04 Exp’tal-05 Exp’tal-06 Exp’tal-07 Exp’tal-08 Strange Attractor The Ω limit set of the flow. There are unstable periodic orbits “in” the strange attractor. They are • “Abundant” • Outline the Strange Attractor • Are the Skeleton of the Strange Attractor Embed-01 Embed-02 Embed-03
Page 1 and 2: The Topology of Chaos Robert Gilmor
Page 3 and 4: Abstract - Key Point The Topology o
Page 5 and 6: Experimental Schematic The Topology
Page 7 and 8: Ask the Masters The Topology of Cha
Page 9 and 10: Real Data The Topology of Chaos Rob
Page 11 and 12: Time Evolution The Topology of Chao
Page 13 and 14: Embeddings The Topology of Chaos Ro
Page 17: More Knotted Embeddings The Topolog
Page 21 and 22: Skeletons The Topology of Chaos Rob
Page 23 and 24: Dynamics and Topology The Topology
Page 25 and 26: Evolution in Phase Space The Topolo
Page 27 and 28: Motion of Blobs in Phase Space The
Page 29 and 30: Fundamental Theorem The Topology of
Page 31 and 32: Fundamental Theorem The Topology of
Page 33 and 34: Birman-Williams Theorem The Topolog
Page 35 and 36: A Mechanism with Symmetry The Topol
Page 37 and 38: Aufbau Princip for Branched Manifol
Page 39 and 40: Dynamics and Topology The Topology
Page 41 and 42: Topological Analysis Program The To
Page 45 and 46: Determine Topological Invariants Th
Page 47 and 48: Determine Topological Invariants Th
Page 49 and 50: Perestroikas of Strange Attractors
Page 51 and 52: Perestroikas of Strange Attractors
Page 53 and 54: An Unexpected Benefit The Topology
Page 55 and 56: Representations The Topology of Cha
Page 57 and 58: Representation Labels The Topology
Page 59 and 60: Inequivalence in R 3 The Topology o
Page 61 and 62: Equivalences The Topology of Chaos
Page 63 and 64: Creating Isotopies The Topology of
Page 65 and 66: Mendeleev’s Table of the Chemical
Page 67 and 68: Stars The Topology of Chaos Robert
Page 69 and 70:
An Experimental Study The Topology
Page 71 and 72:
Basis Set of Orbits The Topology of
Page 73 and 74:
Perestroikas of Branched Manifolds
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Torus and Genus The Topology of Cha
Page 77 and 78:
Flows in Vector Fields The Topology
Page 79 and 80:
Canonical Forms The Topology of Cha
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Labeling Bounding Tori The Topology
Page 83 and 84:
Exponential Growth The Topology of
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Aufbau Princip for Bounding Tori Th
Page 87 and 88:
Poincaré Section The Topology of C
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Represerntation Theory Redux The To
Page 91 and 92:
Embeddings The Topology of Chaos Ro
Page 93 and 94:
Extrinsic Embedding of Bounding Tor
Page 95 and 96:
The Road Ahead The Topology of Chao
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Our Result The Topology of Chaos Ro
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Four Levels of Structure The Topolo
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Page 103 and 104:
Page 105 and 106:
Answered Questions The Topology of
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Unanswered Questions The Topology o
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The Topology of Chaos - Department of Physics - Drexel University

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