Including code to compute Lyapunov exponents for translation surfaces.

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 10 years ago

Code for studying lyapunov exponents of translation surfaces and their covers.

UPDATE:

See compatibility with other existing code for interval echanges and strata compatible with code for quadratic and abelian stratum components

sage: q = QuadraticStratum([7,1,-1,-1,-1,-1]).components()[0]
sage: q.lyapunov_exponents()
[1.0006353514168902,
 0.44659813628011014,
 0.43073741652656045,
 0.2278515712988079,
 0.18675189999010267,
 0.07722243283694208]
sage: q.lyapunov_exponents_H_plus()
[0.44777037675789444, 0.185001855706418]

BUG:

There is a bug for zero lyapunov exponents when decomposing in isotropic components :

sage: import sage.dynamics.flat_surfaces.lyapunov_exponents.interval_exchange as intex
sage: R = intex.cyclic_cover_iet(4, [1, 1, 1, 1])
sage: R.lyapunov_exponents_H_plus()
[0.9996553085103, 0.0007776980910571506, 0.00022201024035355403]
sage: R.lyapunov_exponents_H_plus_isotopic()
[[], [1.0002381322489762], [-0.09753642448496574], [-0.09750440918016302]]

CC: @sagetrac-Fougeroc @videlec

Component: geometry

Keywords: lyapunov_exponents, translation_surfaces, sagedays57

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/16102

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 10 years ago

Description changed:

--- 
+++ 
@@ -7,6 +7,7 @@

+sage: import sage.dynamics.flat_surfaces.lyapunov_exponents.interval_exchange as intex sage: R = intex.cyclic_cover_iet(4, [1, 1, 1, 1]) sage: R.lyapunov_exponents_H_plus() [0.9996553085103, 0.0007776980910571506, 0.00022201024035355403]

videlec commented 10 years ago

comment:2

Hi Charles,

Here are some remarks.

About syntax:

remove trailing whitespaces
documentation lines should be at most 80 characters long
all functions and methods must have an EXAMPLES block. In order to see how much work you have to do, you can use sage -coverage MY_FILE.
The block RETURN should be OUTPUT

General design:

It would be more coherent to have an object "covering of stratum". In a concrete way it would be a permutation of interval exchange (that may be considered as a marking) together with a covering data. We do not care that much about a concrete interval exchange in your code.
avoid using import from sage.all, to know from which module you need to import an object you can use import_statements(MY_OBJECT). For more info look at import_statements?.

About code:

there are already several things in Sage for interval exchange transformations and strata. It would be simpler to use them.
you must put a comment about precision = 128 and diff_sum_seuil = 2**(-precision+20). Even better, remove them.
in order to fit nicely with other components of Sage, you should separate the code (like your class IntExchange) and the examples (like the functions EKZ_example).

videlec commented 10 years ago

Reviewer: Vincent Delecroix

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`20f5170`	`Merge branch 'develop' into lyapunov_exponents`
`bb60056`	`Merge branch '16102/lyapunov_exponents' into lyapunov_exponents`
`5a93d69`	`Merge branch 'develop' of trac.sagemath.org:sage into lyapunov_exponents`
`e2315e7`	`merging with develop`
`ab009e5`	`removed useless files`
`e1129fc`	`remove files`
`ab3a1c4`	`remove file`
`9a37545`	`remove files`
`a47c68c`	`Include test for speed`
`6172656`	`Merge branch 'integrated_lyapunov' into 16102/lyapunov_exponents`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from 048431e to 6172656

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 10 years ago

Changed author from Fougeroc to Charles Fougeron

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 10 years ago

Attachment: compare1100.png

Compare computation of lyapunov exponents wrt number of iteration

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 10 years ago

Compare computation of lyapunov exponents wrt number of iteration (zoom)

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 10 years ago

Attachment: compare40100.png

Attachment: compare_speed.png

Compare log(T)/nb_iterations for diffrent genus and nb_iterations

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 10 years ago

comment:6

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.

This behaviour seems to be responsible for a wrong approximation of lyapunov exponents asymptotically:

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

`02de200`	`Add computation of lyapunov exponents for orientable cover over quadratic stratum.`
`227ce37`	`Merge trac.sagemath.org:sage into 16102/lyapunov_exponents`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from 6172656 to 227ce37

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

`23ee7e7`	`fix bug`
`e91fca7`	`fix bug`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from 227ce37 to e91fca7

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 9 years ago

Description changed:

--- 
+++ 
@@ -1,9 +1,18 @@
 Code for studying lyapunov exponents of translation surfaces and their covers.

-TODO:
-* See compatibility with other existing code for interval echanges and strata
-* It seems to work in most of the examples, 
-  there is a bug for zero lyapunov exponents when decomposing in isotropic components :
+UPDATE:
+* *See compatibility with other existing code for interval echanges and strata*
+  compatible with code for quadratic and abelian stratum components
+
+```
+sage: q = QuadraticStratum([7,1,-1,-1,-1,-1]).components()[0]
+sage: q.lyapunov_exponents()
+sage: q.lyapunov_exponents_H_plus()
+```
+
+
+BUG:
+* There is a bug for zero lyapunov exponents when decomposing in isotropic components :

a67c9e2f-a36c-4a8e-80bb-0c82631d944f commented 9 years ago

Description changed:

--- 
+++ 
@@ -7,7 +7,14 @@

sage: q = QuadraticStratum([7,1,-1,-1,-1,-1]).components()[0] sage: q.lyapunov_exponents() +[1.0006353514168902,

0.44659813628011014,
0.43073741652656045,
0.2278515712988079,
0.18675189999010267,
0.07722243283694208] sage: q.lyapunov_exponents_H_plus() +[0.44777037675789444, 0.185001855706418]

fchapoton commented 9 years ago

comment:12

does not apply, needs rebase

fchapoton commented 8 years ago

Dependencies: #16159

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from e91fca7 to f21ab92

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

f21ab92 Merge branch 'develop' into lyapunov