All Questions
Tagged with nonlinear-dynamics general-topology
8
questions
2
votes
1
answer
112
views
Topological conjugacy of dynamical systems knowing all there periodic orbits
Let's assume we have a discrete dynamical system with $M \subset \mathbb{R}^n$ and
$$x_t=f(x_{t-1}), \text{ where } f: M \rightarrow M \text{ continuous} $$
Let's further assume we know all its cyclic ...
- 661
1
vote
0
answers
46
views
Which figure is homeomorphic to the figure only constructed by all the edges of a cube?
Can someone transform a cube which only has its edges to a figure that is homeomorphic to it?
What is the genus of this figure?
- 87
2
votes
1
answer
173
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Strong non-wandering points and the periodic points
I was looking for something about nonwandering sets and i saw the following definition here: A question about non-wandering points :
Let $f:X\to X$ be a homeomorphism of a compact metric space $(X, d)...
- 3,201
3
votes
2
answers
282
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No homeomorphism of the interval $[0,1]$ is topologically mixing
I am trying to show that there is no homeomorphism $f:[0,1] \to [0,1]$ which is topologically mixing (a dynamical system $T:X\to X$ is called topologically mixing, provided, for every pair of open ...
- 3,201
1
vote
1
answer
87
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Topologically Transitive Flow on $R^n$
I have been looking but cannot find the following: an example of a topologically transitive map on $\mathbb{S}^n$ or on $\mathbb{R}^n$ (for arbitrary $n$). Here, by a topologically transitive flow, I ...
- 6,779
1
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0
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602
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Is topological semi-conjugacy sufficient for the case described below, or does one need full conjugacy?
I'm taking an undergraduate course in nonlinear dynamics, and the idea of topological conjugacy between (one-dimensional) iterated maps was introduced as follows:
Let ${I}$ and ${J}$ be intervals. We ...
7
votes
1
answer
183
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Generalisation of Index of a curve to higher dimensions
Im studying Non Linear Dynamics and Chaos from Strogatz's textbook. In the sixth chapter, while talking about non linear flows in 2 dimensions he introduces the index of a curve in a vector field and ...
- 3,560
1
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0
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41
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construction of henon map
I am trying to construct a suspension that will model the Henon map.
So far I have the suspension $\dot\phi=lnA\phi$ which is a linear suspension of a mapping A. The solution to this is $\phi=e^{...
