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1 vote
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• 11.1k
1 vote
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### Is there a source out there which works out a Hartman-Grobman-type theorem on a manifold?

But, of course, it is a purely local result. For manifolds, see for instance Ch. 2, Theorem 4.1 in Palis, Jacob jun.; de Melo, Welington, Geometric theory of dynamical systems. An introduction. Transl....
• 103k
1 vote

### Equation for the Logarithmic Spiral from a vertex to the Brocard Point

Fig. 1 : With the triangle taken as second example in the answer given by @disgraced. I have an error in my code because there should be an agreement on the curves. I will attempt to spot it and ...
• 84.5k
1 vote

### References on Kolmogorov-Sinai (measure-theoretic) entropy and convergence of measures

This is nowhere close to a full answer, but a place you can read about this is in Peter Walters book, "An introduction to ergodic theory". Specifically, he discusses in chapter 8.1 ...
• 7,930
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### Equation for the Logarithmic Spiral from a vertex to the Brocard Point

Given $\triangle ABC$, you first compute the Brocard angle $\omega$ from the equation: $\cot \omega = \cot A + \cot B + \cot C$ Next, if you scale $\triangle ABC$ by a scale factor $\alpha \lt 1$ ...
• 25k

### Compute the number of ways the frog can move from A to B.

Alternative approach, which is based on partitioning an integer. To partition $~5~$ into terms all less than 3: P5a: 2 - 2 - 1 P5b: 2 - 1 - 1 - 1 P5c: 1 - 1 - 1 - 1 - 1 To partition $~6~$ into ...
• 38k

### Compute the number of ways the frog can move from A to B.

This is not a 3D DP problem (in an algorithm sense) given the constraint that the frog can't move $k$ steps in the same direction consecutively ($k=3$ in this case), because the state of the frog is ...
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• 34.7k

### Why does the output of a stable LTI system approach the input mathematically speaking?

Assuming that the input $x$ is very slowly moving relative to the real parts of the eigenvalues (and their implied decay rates or half-life), then the excitation of the left side from time step to ...
• 129k
1 vote
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### Proof of Lemma 4.1.3 in 'Translation Surfaces' by Masur and Athreya

You seem to be right; simply merging the last two sentences and editing as follows seems sufficient: "... or $q'$ does, in which case $p$ returns to $\beta$ at time $t_1-t_0$." For reference ...
• 11.1k
1 vote
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### Incorrect use of Bendixson-Dulac theorem?

Your proof looks correct to me. The system does not have a limit cycle as the trajectories are not bounded. I looked over the paper to see if I could find the error. The paper's authors argue as ...
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