Math 145 Chaos Theory Ralph Abraham www.ralph-abraham.org Math - - PowerPoint PPT Presentation

▶
math 145 chaos theory
SMART_READER_LITE
LIVE PREVIEW

Math 145 Chaos Theory Ralph Abraham www.ralph-abraham.org Math - - PowerPoint PPT Presentation

Jun 25, 2023 350 likes •989 views

Math 145 Chaos Theory Ralph Abraham www.ralph-abraham.org Math Dept, UCSC Spring 2017 Meeting #5Th, May 4 3D Flows, continued Dynamics: The Geometry of Behavior Part 3: Global Behavior Chs. 13, 14, and 15 Ch. 13:

slide-1
SLIDE 1

Math 145 Chaos Theory

Ralph Abraham www.ralph-abraham.org Math Dept, UCSC Spring 2017

slide-2
SLIDE 2

Meeting #5Th, May 4

  • 3D Flows, continued
  • Dynamics: The Geometry of Behavior
  • Part 3: Global Behavior
  • Chs. 13, 14, and 15
slide-3
SLIDE 3
  • Ch. 13: Heteroclinic Tangles
  • Sec. 13.1. Point to point
  • Sec. 13.2. The Lorenz attractor
  • Sec. 13.3. Point to cycle
  • Sec. 13.4. Cycle to cycle
  • Sec. 13.5. Birkhoff’s signature
slide-4
SLIDE 4
  • Sec. 13.1

Point to Point

slide-5
SLIDE 5
slide-6
SLIDE 6
slide-7
SLIDE 7
slide-8
SLIDE 8
slide-9
SLIDE 9
slide-10
SLIDE 10
slide-11
SLIDE 11
slide-12
SLIDE 12
  • Sec. 13.2

The Lorenz Attractor

slide-13
SLIDE 13
slide-14
SLIDE 14
slide-15
SLIDE 15
slide-16
SLIDE 16
slide-17
SLIDE 17
slide-18
SLIDE 18
slide-19
SLIDE 19
slide-20
SLIDE 20
slide-21
SLIDE 21
  • Sec. 13.3

Point to Cycle

slide-22
SLIDE 22
slide-23
SLIDE 23
slide-24
SLIDE 24
slide-25
SLIDE 25
slide-26
SLIDE 26
slide-27
SLIDE 27
  • Sec. 13.4

Cycle to Cycle

slide-28
SLIDE 28
slide-29
SLIDE 29
slide-30
SLIDE 30
slide-31
SLIDE 31
  • Sec. 13.5

Birkhoff’s Signature

slide-32
SLIDE 32
slide-33
SLIDE 33
slide-34
SLIDE 34
slide-35
SLIDE 35
slide-36
SLIDE 36
slide-37
SLIDE 37
slide-38
SLIDE 38
slide-39
SLIDE 39
  • Ch. 14: Homoclinic Tangles
  • Sec. 14.1. Homoclinic cycles
  • Sec. 14.3. Horseshoes
slide-40
SLIDE 40
  • Sec. 14.1

Homoclinic Cycles

slide-41
SLIDE 41
slide-42
SLIDE 42
slide-43
SLIDE 43
slide-44
SLIDE 44
slide-45
SLIDE 45
slide-46
SLIDE 46
slide-47
SLIDE 47
slide-48
SLIDE 48
slide-49
SLIDE 49
slide-50
SLIDE 50
  • Sec. 14.3

Horseshoes

slide-51
SLIDE 51
slide-52
SLIDE 52
slide-53
SLIDE 53
slide-54
SLIDE 54
slide-55
SLIDE 55
slide-56
SLIDE 56
slide-57
SLIDE 57
slide-58
SLIDE 58
  • Ch. 15: Recurrence
  • Sec. 15.3. Nonwandering points
slide-59
SLIDE 59
  • Sec. 15.3

Nonwandering Points

slide-60
SLIDE 60
slide-61
SLIDE 61
slide-62
SLIDE 62

Math 145 Spring 2017 Meeting #5Th

End