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Results tagged with ds.dynamical-systems
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user 1004
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
23
votes
Accepted
A question of Erdős on equidistribution
The statement was shown to be false by J. Bourgain in a paper published in 1988 (Almost Sure Convergence and Bounded Entropy, doi:10.1007/BF02765022). Well before either Harman's 1997 book and the 200 …
- 17.1k
13
votes
Accepted
The functional equation $f(f(x))=x+f(x)^2$
Having thought about this question some more, including making some plots of the trajectories of points under iterated applications of $f$ (see Gottfried's circular trajectories), it is possible to de …
- 1,228
11
votes
Accepted
Does there exist a shot in ideal pocket billiards?
How about the following? It suggests the answer to Q1 is no.
The 2,15,6,9 and cueball are in a horizontal row and touching (or very nearly touching). The 14,cueball and 4 are in a vertical row and (v …
- 151k
27
votes
Accepted
Integrability of the Cohen map
I have run some simple simulations of this system in Python, and it looks nothing like a nice integrable system once you zoom in on the orbits. Certainly, the orbits do not look like closed curves abo …
- 151k