Medijski sadržaj
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working on a new project...
#dynomaticpic.twitter.com/w3gYEzZXa5
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he was socially awkward in that clearly-brilliant way. we just all thought he was weird. then, one day, there was an announcement for a research talk in the math department that had a funny picture: (image credit https://www.math.uni-tuebingen.de/user/nick/gallery/WenteTorus.html …)pic.twitter.com/Sbo5xCH19k
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this semester, i am teaching multivariable calculus for engineers
@penn, using materials from the Calculus BLUE Project, a video-text on youtube. you can check out the (updated for 2020) trailer here...https://www.youtube.com/watch?v=xZeqTptJ0xY … -
like all things, this semester has come to an end... final lecture of my applied dynamical systems course
@Pennpic.twitter.com/ohbDPHV29V
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@_jakobhansen just won the Carlitz-Zippin prize for best thesis in math at Penn, for work on Hodge Laplacians for cellular sheaves...!pic.twitter.com/RPldSycbyY – mjesto: David Rittenhouse Laboratory
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gravitational 3-body problems are great for chaotic dynamics. one of my favorites is the sitnikov system: given two equal massive bodies rotating about one another on ellipses, add a third tiny mass perfectly poised between them. give it a kick & what happens?pic.twitter.com/fn8ZSHF1kO
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the latest video by
@veritasium on dynamical systems features a few of my recent animations :-)https://www.youtube.com/watch?v=fDek6cYijxI … -
surprise! twitter video compression sucks... for a decent (and embeddable) version of this vid, go to the original on YT:https://youtu.be/lVdVCd8BGdU
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one of the things you notice when you study chaotic dynamics in 2-d maps is the resemblance to mixing of fluids. the stretching & folding mechanisms are very similar.pic.twitter.com/5zBnkjpbip
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the poincare map of this system -- the first-return map obtained by slicing along a transverse disc -- has lots of interesting dynamics, including horseshoes.pic.twitter.com/HFEvjCJJv4
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the periodically-forced duffing oscillator induces a flow on the solid torus with some lovely chaotic dynamics. by following a set of initial conditions in the plane over time, you can see the stretching & folding lead to chaos.pic.twitter.com/q10YvrWf1f
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this week in dynamical systems: examples of chaotic systems... i'm going to review one of my favorite -- the forced duffing oscillator. here is a physical simulation of it using springs to model the double-well potential.pic.twitter.com/1yYzMWHKa5
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The desserts were especially nice, thanks to the 12yo who made chocolates...pic.twitter.com/xpvpFv9mP4
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We had about eighteen students who had no way of getting home show up.pic.twitter.com/haRX08P82l
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A view of the appetizer course... Baked a dozen loaves of bread.pic.twitter.com/9ZKUUl7IvU
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Having a great time hosting
@Penn students at my home for Thanksgiving... For some of them, it's their first Thanksgiving ever!pic.twitter.com/VB1UmMgpww
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today in dynamics class we learned about generalizations of the smale horseshoe map to maps with a *markov partition* defined via horizontal and vertical strips. these lead to subshifts of finite type & lots of cool theory...pic.twitter.com/noq8g3zEO2
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twitter is going to compress this into mush, i'm sure. there is a better quality version up on youtube:https://youtu.be/skvCUST4LPk
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the invariant set of the smale horseshoe is obtained by intersecting all the horizontal & vertical strips in the square under iterations of the map & its inverse. this type of set is a cantor set. it looks like dust, but is uncountably infinite.pic.twitter.com/2wz7Q3cFeo
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