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Results tagged with ds.dynamical-systems
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user 6514
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
5
votes
2
answers
594
views
How do we recognize a Markov partition?
I'm looking for theorems that can be used to show that a topological partition for a given expanding map is Markov. Here are the relevant definitions:
Let $\phi\colon\mathbb{R}^m\to\mathbb{R}^m$ be …
- 8,483
2
votes
Accepted
Fine structure of bifurcation diagram of logistic family
The questions you are asking are fundamental to the theory of one-dimensional dynamical systems. I would suggest starting with an introductory textbook, such as An Introduction to Chaotic Dynamical S …
- 8,483
23
votes
Accepted
How is the Julia set of $fg$ related to the Julia set of $gf$?
I'm not sure if this is helpful, but here is an example. The following picture shows the filled Julia set for $z^6 - 1$.
and the following picture shows the filled Julia set for $(z^2-1)^3$:
Th …
- 8,483
229
votes
Accepted
Perfectly centered break of a perfectly aligned pool ball rack
This question was cross-posted on Math Stack Exchange. Here is a copy of my answer for it there.
This is it. The perfectly centered billiards break. Behold.
Setup
This break was computed i …
- 8,483