3 ms·

Is there a book about this? This isnt covered that deep in Dif.Eq. books...

by gatane 4y ago

squaredot 4y ago
Maybe the most famous is the Lorenz attractor, arising from the Lorenz System (this is one of the simulations shown in the website). In Wikipedia you find a description of the system https://en.wikipedia.org/wiki/Lorenz_system https://en.wikipedia.org/wiki/Lorenz_system
kkylin 4y ago
James Gleick's "Chaos" remains, in my view, a great popular book on the subject, and manages to convey many of the ideas at a conceptual level without getting technical. And if you enjoy that, you might also like Strogatz's "Sync." For slightly more technical treatment, Strogatz's Nonlinear Dynamics and Chaos is now a standard text. It isn't terribly technical and is quite well written and (in my view) easy to read for anyone with a background in vector calculus, diff eqs, & perhaps a little bit of linear algebra. (There are now other good options to, some more mathematical and some more application-oriented, but I still think Strogatz is a good place to start.)
- azepoi 4y ago
  Can you expand on the last part? I mean the good other technical books for someone already a bit familiar who wants a deeper dive? Thanks for the pointers
- edbaskerville 4y ago
  Second Strogatz, does an amazing job linking the math to the visual intuition--probably less rigorous than some texts, but the perfect balance for an intro. Took an amazing course based on that book with Charlie Doering, who has sadly passed. He could draw multicolor, qualitatively-correct 3D attractors freehand on a chalkboard while helpfully narrating the system dynamics.
lanstin 4y ago
The Topology of Chaos, https://www.amazon.com/Topology-Chaos-Alice-Stretch-Squeezeland/dp/3527410678/ https://www.amazon.com/Topology-Chaos-Alice-Stretch-Squeezel... is a good modern book on it. It is a fun problem because it stems from continuous diff eq but the answers come from topological analysis around the fixed sets, and the ways fixed sets can change as continuous parameters change.
bmitc 4y ago
* Chaos and Dynamical Systems by David Feldman * Exploring Chaos: Theory and Experiment by Brian Davies * Chaos: From Theory to Applications by A.A. Tsonis * Chaos and Fractals: An Elementary Introduction by David Feldman * Nonlinear Dynamics And Chaos by Tufillaro, Abbott, Reilly * Computers, pattern, chaos, and beauty: Graphics from an unseen world by Clifford Pickover * A First Course In Chaotic Dynamical Systems by Robert Devaney Just some references from my "to read" collection.
rikroots 4y ago
Not a book, but Paul Bourke's website - Fractals, Chaos, Self-Similarity - has a wealth of information. http://paulbourke.net/fractals/ http://paulbourke.net/fractals/
peapicker 4y ago
"Strange Attractors: Creating Patterns in Chaos" by Julien C. Sprott. I am lucky enough to have a 1st edition print, but there is now a free PDF online: https://sprott.physics.wisc.edu/SA.HTM https://sprott.physics.wisc.edu/SA.HTM

Is there a book about this? This isnt covered that deep in Dif.Eq. books...

by gatane 4y ago

Is there a book about this? This isnt covered that deep in Dif.Eq. books...

Maybe the most famous is the Lorenz attractor, arising from the Lorenz System (this is one of the simulations shown in the website). In Wikipedia you find a description of the system https://en.wikipedia.org/wiki/Lorenz_system https://en.wikipedia.org/wiki/Lorenz_system

kkylin 4y ago

James Gleick's "Chaos" remains, in my view, a great popular book on the subject, and manages to convey many of the ideas at a conceptual level without getting technical. And if you enjoy that, you might also like Strogatz's "Sync." For slightly more technical treatment, Strogatz's Nonlinear Dynamics and Chaos is now a standard text. It isn't terribly technical and is quite well written and (in my view) easy to read for anyone with a background in vector calculus, diff eqs, & perhaps a little bit of linear algebra. (There are now other good options to, some more mathematical and some more application-oriented, but I still think Strogatz is a good place to start.)

azepoi 4y ago
Can you expand on the last part? I mean the good other technical books for someone already a bit familiar who wants a deeper dive? Thanks for the pointers
edbaskerville 4y ago
Second Strogatz, does an amazing job linking the math to the visual intuition--probably less rigorous than some texts, but the perfect balance for an intro. Took an amazing course based on that book with Charlie Doering, who has sadly passed. He could draw multicolor, qualitatively-correct 3D attractors freehand on a chalkboard while helpfully narrating the system dynamics.

lanstin 4y ago

The Topology of Chaos, https://www.amazon.com/Topology-Chaos-Alice-Stretch-Squeezeland/dp/3527410678/ https://www.amazon.com/Topology-Chaos-Alice-Stretch-Squeezel... is a good modern book on it. It is a fun problem because it stems from continuous diff eq but the answers come from topological analysis around the fixed sets, and the ways fixed sets can change as continuous parameters change.

bmitc 4y ago

* Chaos and Dynamical Systems by David Feldman * Exploring Chaos: Theory and Experiment by Brian Davies * Chaos: From Theory to Applications by A.A. Tsonis * Chaos and Fractals: An Elementary Introduction by David Feldman * Nonlinear Dynamics And Chaos by Tufillaro, Abbott, Reilly * Computers, pattern, chaos, and beauty: Graphics from an unseen world by Clifford Pickover * A First Course In Chaotic Dynamical Systems by Robert Devaney Just some references from my "to read" collection.

rikroots 4y ago

Not a book, but Paul Bourke's website - Fractals, Chaos, Self-Similarity - has a wealth of information. http://paulbourke.net/fractals/ http://paulbourke.net/fractals/

peapicker 4y ago

"Strange Attractors: Creating Patterns in Chaos" by Julien C. Sprott. I am lucky enough to have a 1st edition print, but there is now a free PDF online: https://sprott.physics.wisc.edu/SA.HTM https://sprott.physics.wisc.edu/SA.HTM