The Resource A first course in chaotic dynamical systems : theory and experiment, Robert L. Devaney

A first course in chaotic dynamical systems : theory and experiment, Robert L. Devaney

Label
A first course in chaotic dynamical systems : theory and experiment
Title
A first course in chaotic dynamical systems
Title remainder
theory and experiment
Statement of responsibility
Robert L. Devaney
Creator
Subject
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1948-
http://library.link/vocab/creatorName
Devaney, Robert L.
Illustrations
illustrations
Index
index present
LC call number
QA614.8
LC item number
.D49 1992
Literary form
non fiction
Nature of contents
bibliography
Series statement
Studies in nonlinearity
http://library.link/vocab/subjectName
  • Differentiable dynamical systems
  • Chaotic behavior in systems
  • Chaotic behavior in systems
  • Differentiable dynamical systems
  • Sistemas Dinamicos
  • Chaos (théorie des systèmes)
  • Dynamique différentiable
  • Chaos
  • Chaotisches System
  • Differenzierbares dynamisches System
  • Dynamisches System
Label
A first course in chaotic dynamical systems : theory and experiment, Robert L. Devaney
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 295-298) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Ch. 1. A Mathematical and Historical Tour. 1.1. Images from Dynamical Systems. 1.2. A Brief History of Dynamics -- Ch. 2. Examples of Dynamical Systems. 2.1. An Example from Finance. 2.2. An Example from Ecology. 2.3. Finding Roots and Solving Equations. 2.4. Differential Equations -- Ch. 3. Orbits. 3.1. Iteration. 3.2. Orbits. 3.3. Types of Orbits. 3.4. Other Orbits. 3.5. The Doubling Function. 3.6. Experiment: The Computer May Lie -- Ch. 4. Graphical Analysis. 4.1. Graphical Analysis. 4.2. Orbit Analysis. 4.3. The Phase Portrait -- Ch. 5. Fixed and Periodic Points. 5.1. A Fixed Point Theorem. 5.2. Attraction and Repulsion. 5.3. Calculus of Fixed Points. 5.4. Why Is This True? 5.5. Periodic Points. 5.6. Experiment: Rates of Convergence -- Ch. 6. Bifurcations. 6.1. Dynamics of the Quadratic Map. 6.2. The Saddle-Node Bifurcation. 6.3. The Period-Doubling Bifurcation. 6.4. Experiment: The Transition to Chaos -- Ch. 7. The Quadratic Family. 7.1. The Case c = -2. 7.2. The Case c [actual symbol not reproducible] -2. 7.3. The Cantor Middle-Thirds Set -- Ch. 8. Transition to Chaos. 8.1. The Orbit Diagram. 8.2. The Period-Doubling Route to Chaos. 8.3. Experiment: Windows in the Orbit Diagram -- Ch. 9. Symbolic Dynamics. 9.1. Itineraries. 9.2. The Sequence Space. 9.3. The Shift Map. 9.4. Conjugacy -- Ch. 10. Chaos. 10.1. Three Properties of a Chaotic System. 10.2. Other Chaotic Systems. 10.3. Manifestations of Chaos. 10.4. Experiment: Feigenbaum's Constant -- Ch. 11. Sarkovskii's Theorem. 11.1. Period 3 Implies Chaos. 11.2. Sarkovskii's Theorem. 11.3. The Period 3 Window. 11.4. Subshifts of Finite Type -- Ch. 12. The Role of the Critical Orbit. 12.1. The Schwarzian Derivative. 12.2. The Critical Point and Basins of Attraction -- Ch. 13. Newton's Method. 13.1. Basic Properties. 13.2. Convergence and Nonconvergence -- Ch. 14. Fractals. 14.1. The Chaos Game. 14.2. The Cantor Set Revisited. 14.3. The Sierpinski Triangle. 14.4. The Koch Snowflake. 14.5. Topological Dimension. 14.6. Fractal Dimension. 14.7. Iterated Function Systems. 14.8. Experiment: Iterated Function Systems -- Ch. 15. Complex Functions. 15.1. Complex Arithmetic. 15.2. Complex Square Roots. 15.3. Linear Complex Functions. 15.4. Calculus of Complex Functions -- Ch. 16. The Julia Set. 16.1. The Squaring Function. 16.2. The Chaotic Quadratic Function. 16.3. Cantor Sets Again. 16.4. Computing the Filled Julia Set. 16.5. Experiment: Filled Julia Sets and Critical Orbits. 16.6. The Julia Set as a Repellor -- Ch. 17. The Mandelbrot Set. 17.1. The Fundamental Dichotomy. 17.2. The Mandelbrot Set. 17.3. Experiment: Periods of Other Bulbs. 17.4. Experiment: Periods of the Decorations. 17.5. Experiment: Find the Julia Set. 17.6. Experiment: Spokes and Antennae. 17.7. Experiment: Similarity of the Mandelbrot and Julia Sets -- Ch. 18. Further Projects and Experiments. 18.1. The Tricorn. 18.2. Cubics. 18.3. Exponential Functions. 18.4. Trigonometric Functions. 18.5. Complex Newton's Method -- Appendix A. Mathematical Preliminaries -- Appendix B. Algorithms -- Appendix C. References
Dimensions
24 cm.
Extent
xi, 302 pages
Isbn
9780201554069
Lccn
91038310
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations (some color)
System control number
  • (OCoLC)24695575
  • (OCoLC)ocm24695575
Label
A first course in chaotic dynamical systems : theory and experiment, Robert L. Devaney
Publication
Bibliography note
Includes bibliographical references (p. 295-298) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Ch. 1. A Mathematical and Historical Tour. 1.1. Images from Dynamical Systems. 1.2. A Brief History of Dynamics -- Ch. 2. Examples of Dynamical Systems. 2.1. An Example from Finance. 2.2. An Example from Ecology. 2.3. Finding Roots and Solving Equations. 2.4. Differential Equations -- Ch. 3. Orbits. 3.1. Iteration. 3.2. Orbits. 3.3. Types of Orbits. 3.4. Other Orbits. 3.5. The Doubling Function. 3.6. Experiment: The Computer May Lie -- Ch. 4. Graphical Analysis. 4.1. Graphical Analysis. 4.2. Orbit Analysis. 4.3. The Phase Portrait -- Ch. 5. Fixed and Periodic Points. 5.1. A Fixed Point Theorem. 5.2. Attraction and Repulsion. 5.3. Calculus of Fixed Points. 5.4. Why Is This True? 5.5. Periodic Points. 5.6. Experiment: Rates of Convergence -- Ch. 6. Bifurcations. 6.1. Dynamics of the Quadratic Map. 6.2. The Saddle-Node Bifurcation. 6.3. The Period-Doubling Bifurcation. 6.4. Experiment: The Transition to Chaos -- Ch. 7. The Quadratic Family. 7.1. The Case c = -2. 7.2. The Case c [actual symbol not reproducible] -2. 7.3. The Cantor Middle-Thirds Set -- Ch. 8. Transition to Chaos. 8.1. The Orbit Diagram. 8.2. The Period-Doubling Route to Chaos. 8.3. Experiment: Windows in the Orbit Diagram -- Ch. 9. Symbolic Dynamics. 9.1. Itineraries. 9.2. The Sequence Space. 9.3. The Shift Map. 9.4. Conjugacy -- Ch. 10. Chaos. 10.1. Three Properties of a Chaotic System. 10.2. Other Chaotic Systems. 10.3. Manifestations of Chaos. 10.4. Experiment: Feigenbaum's Constant -- Ch. 11. Sarkovskii's Theorem. 11.1. Period 3 Implies Chaos. 11.2. Sarkovskii's Theorem. 11.3. The Period 3 Window. 11.4. Subshifts of Finite Type -- Ch. 12. The Role of the Critical Orbit. 12.1. The Schwarzian Derivative. 12.2. The Critical Point and Basins of Attraction -- Ch. 13. Newton's Method. 13.1. Basic Properties. 13.2. Convergence and Nonconvergence -- Ch. 14. Fractals. 14.1. The Chaos Game. 14.2. The Cantor Set Revisited. 14.3. The Sierpinski Triangle. 14.4. The Koch Snowflake. 14.5. Topological Dimension. 14.6. Fractal Dimension. 14.7. Iterated Function Systems. 14.8. Experiment: Iterated Function Systems -- Ch. 15. Complex Functions. 15.1. Complex Arithmetic. 15.2. Complex Square Roots. 15.3. Linear Complex Functions. 15.4. Calculus of Complex Functions -- Ch. 16. The Julia Set. 16.1. The Squaring Function. 16.2. The Chaotic Quadratic Function. 16.3. Cantor Sets Again. 16.4. Computing the Filled Julia Set. 16.5. Experiment: Filled Julia Sets and Critical Orbits. 16.6. The Julia Set as a Repellor -- Ch. 17. The Mandelbrot Set. 17.1. The Fundamental Dichotomy. 17.2. The Mandelbrot Set. 17.3. Experiment: Periods of Other Bulbs. 17.4. Experiment: Periods of the Decorations. 17.5. Experiment: Find the Julia Set. 17.6. Experiment: Spokes and Antennae. 17.7. Experiment: Similarity of the Mandelbrot and Julia Sets -- Ch. 18. Further Projects and Experiments. 18.1. The Tricorn. 18.2. Cubics. 18.3. Exponential Functions. 18.4. Trigonometric Functions. 18.5. Complex Newton's Method -- Appendix A. Mathematical Preliminaries -- Appendix B. Algorithms -- Appendix C. References
Dimensions
24 cm.
Extent
xi, 302 pages
Isbn
9780201554069
Lccn
91038310
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations (some color)
System control number
  • (OCoLC)24695575
  • (OCoLC)ocm24695575

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