#16102: Including code to compute Lyapunov exponents for translation surfaces.
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Reporter: Fougeroc | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-6.3
Component: geometry | Resolution:
Keywords: | Merged in:
lyapunov_exponents, | Reviewers: Vincent Delecroix
translation_surfaces, geometry, | Work issues:
sagedays57 | Commit:
Authors: Charles Fougeron | 61726567f284b07d4f7495081d9856d70c0974d9
Report Upstream: N/A | Stopgaps:
Branch: |
u/Fougeroc/Lyapunov_exponents_for_translation_surfaces|
Dependencies: |
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Comment (by Fougeroc):
I updated the code which integrate the computation of lyapunov exponents
for quadratic strata.
You can now use the function :
{{{
stratum_component = QuadraticStratum([1]*8 + [-1]*4).components()[0]
stratum_component.orientable_cover().lyapunov_exponents_H_plus()
}}}
I noticed a strange behaviour while doing some computeur simulations for
asymptotic of lyapunov exponents. When genus is getting bigger (and
consequently the number of intervals), the speed is decreasing. While
increasing the number of iteration, log(t)/n is also increasing. A
surprising behaviour (possibly due to float approximation) is that the
there is a limit value for this function for a large value of genus.
[[Image(compare_speed.png)]]
This behaviour seems to be responsible for a wrong approximation of
lyapunov exponents asymptotically:
[[Image(compare1_100_.png)]]
[[Image(compare40_100_.png)]]
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Ticket URL: <http://trac.sagemath.org/ticket/16102#comment:6>
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