Projet Dyna3S » Comp

Main.Comp History

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February 20, 2017, at 03:14 PM by 172.23.131.187 -
Changed lines 34-35 from:
**Ergodic properties of the generic trajectories
 Borel-Berstein type theorem, Khinchine type theorem
to:
**Ergodic properties of the generic trajectories: Borel-Berstein type theorem, Khinchine type theorem
February 20, 2017, at 03:14 PM by 172.23.131.187 -
Changed lines 26-27 from:
**Lypunov exponents
to:
**Lyapunov exponents
Changed lines 31-32 from:
to:
**Minkowski question mark. See [[https://en.wikipedia.org/wiki/Minkowski's_question_mark_function| Wikipedia]] and  the [[https://arxiv.org/abs/math/0210480|paper]] by O. R. Beaver and T. Garrity.
Changed lines 46-47 from:
*Minkowski question mark
**See [[https://en.wikipedia.org/wiki/Minkowski's_question_mark_function| Wikipedia]] and  the [[https://arxiv.org/abs/math/0210480|paper]] by O. R. Beaver and T. Garrity.
to:
*Geodesic flow on the modular surface
February 20, 2017, at 03:12 PM by 172.23.131.187 -
Changed line 46 from:
**See the paper [[https://arxiv.org/abs/math/0210480|paper]] by O. R. Beaver and T. Garrity.
to:
**See [[https://en.wikipedia.org/wiki/Minkowski's_question_mark_function| Wikipedia]] and  the [[https://arxiv.org/abs/math/0210480|paper]] by O. R. Beaver and T. Garrity.
February 20, 2017, at 03:09 PM by 172.23.131.187 -
Changed lines 42-52 from:
**Properties of the symbolic shift:
        factor complexity, balancedness, Pisot property for finite products, weak
mixing.






*Random behaviour when any elementary  matrix can be used. Same for TRIP maps
.

to:
**Properties of the symbolic shift: factor complexity, balancedness, Pisot property for finite products, weak mixing.

Changed lines 46-52 from:

*Reachable columns/matrices. Monoid generated by allowed porducts of matrices.

*Properties of the symbolic  shift: factor complexity, balancedness, Pisot property for finite products, weak mixing
.

*Comparison of the  statistical/ergodic properties of finite and periodic orbits with  generic ones.
to:
**See the paper [[https://arxiv.org/abs/math/0210480|paper]] by O. R. Beaver and T. Garrity.


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Deleted line 52:
February 20, 2017, at 03:06 PM by 172.23.131.187 -
Changed line 20 from:
**Definition of a ''good'' functional spa
to:
**Definition of a ''good'' functional space
Changed lines 46-48 from:
*Algebraic characterization of periodic expansions

*Detection of linear dependence for the coordinates of the  vector to be expanded
to:

February 20, 2017, at 03:04 PM by 172.23.131.187 -
Deleted line 8:
Changed lines 10-16 from:
*Convergence (weak or strong).

*Ergodic properties
**Invariant measure, natural extension. See the 
[[https://arxiv.org/abs/1508.07814|paper]]  by P. Arnoux, S. Labbé.
**Properties of transfer operator

*Diophantine
properties
to:

*Properties of the underlying dynamical system
**Existence of a natural extension. See the 
[[https://arxiv.org/abs/1508.07814|paper]]  by P. Arnoux, S. Labbé.
**Invariant measure: existence of an explicit expression 

 



*Properties of the transfer operator
**Definition of a ''good'' functional spa
**Quasi-compactness or other ''good'' propertie
**UNI  property

*Convergence of the algorithm (weak or strong)
*
*Diophantine properties
Changed lines 27-28 from:
**Metric number theory: Borel-Berstein type theorem, Khinchine type theorem
to:

*Particular trajectories
**Algebraic characterization of periodic  trajectories
**Detection of linear dependence for the coordinates of the  input vector

*Metric number theory
**Ergodic properties of the generic trajectories
 Borel-Berstein type theorem, Khinchine type theorem
**Probabilistic properties of truncated generic trajectories. Existence of limit Gaussian laws, etc...
**Comparison of the probabilistic  properties of finite and/or periodic trajectories with generic ones.


*Properties of associated matrices
**Reachable columns/matrices. Monoid generated by allowed products of matrices.
**Random behaviour when any elementary matrix can be used. Same for TRIP maps.
**Properties of the symbolic shift:
        factor complexity, balancedness, Pisot property for finite products, weak mixing.


Deleted line 49:
*Possible projectivizations
February 20, 2017, at 02:59 PM by 172.23.131.187 -
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*Description
to:
*General description
Added line 10:
**Possible projectivizations
February 09, 2017, at 12:13 PM by 172.23.131.187 -
Changed line 35 from:
*Comparison of the  staistical/ergodci properties of finite and periodic orbits with  generic ones.
to:
*Comparison of the  statistical/ergodic properties of finite and periodic orbits with  generic ones.
February 09, 2017, at 12:10 PM by 172.23.131.187 -
February 09, 2017, at 12:05 PM by 172.23.131.187 -
Changed lines 10-11 from:
to:
*Convergence (weak or strong).
Added lines 34-35:

*Comparison of the  staistical/ergodci properties of finite and periodic orbits with  generic ones.
February 09, 2017, at 12:00 PM by 172.23.131.187 -
Added lines 30-33:
*Reachable columns/matrices. Monoid generated by allowed porducts of matrices.

*Properties of the symbolic  shift: factor complexity, balancedness, Pisot property for finite products, weak mixing.

Deleted line 41:
*Reachable columns/matrices. Monoid generated by allowed porducts of matrices.
February 09, 2017, at 11:59 AM by 172.23.131.187 -
Added lines 27-29:

*Minkowski question mark

Changed line 38 from:
*Minkowski question mark
to:
*Reachable columns/matrices. Monoid generated by allowed porducts of matrices.
February 09, 2017, at 11:56 AM by 172.23.131.187 -
Changed lines 23-26 from:
to:
*Possible projectivizations

*Random behaviour when any elementary  matrix can be used. Same for TRIP maps.

Changed lines 33-35 from:
**Addition chains
to:
**Addition chains

*Minkowski question mark
February 09, 2017, at 11:49 AM by 172.23.131.187 -
Changed line 12 from:
**Invariant measure, natural extension. See the  [[https://arxiv.org/abs/1508.07814|paper]  by P. Arnoux, S. Labbé.
to:
**Invariant measure, natural extension. See the  [[https://arxiv.org/abs/1508.07814|paper]]  by P. Arnoux, S. Labbé.
February 09, 2017, at 11:49 AM by 172.23.131.187 -
Changed line 12 from:
**Invariant measure, natural extension
to:
**Invariant measure, natural extension. See the  [[https://arxiv.org/abs/1508.07814|paper]  by P. Arnoux, S. Labbé.
February 09, 2017, at 11:47 AM by 172.23.131.187 -
Added line 8:
How to define a multiplicative form?  see e.g. T. Garrity's approach.
December 13, 2016, at 04:49 AM by 130.130.136.80 -
Added lines 26-27:

**Gcd computation
December 13, 2016, at 04:48 AM by 130.130.136.80 -
Changed lines 3-4 from:
Terminology: see the papers by T. Garrity. See also the [[Attach:16-Garrity.pdf |note]] by T. Garrity.
to:
Terminology: see the papers by T. Garrity. See also the [[Attach:16-Garrity.pdf |note]] by T. Garrity
and the [[https://arxiv.org/abs/1511.08399|cheat sheet]] by S. Labbé.
December 13, 2016, at 04:46 AM by 130.130.136.80 -
Changed line 3 from:
Terminology: see the papers by T. Garrity. See also the [[ |note]] by T. Garrity.
to:
Terminology: see the papers by T. Garrity. See also the [[Attach:16-Garrity.pdf |note]] by T. Garrity.
December 13, 2016, at 04:45 AM by 130.130.136.80 -
Changed line 3 from:
Terminology: see the papers by T. Garrity
to:
Terminology: see the papers by T. Garrity. See also the [[ |note]] by T. Garrity.
December 08, 2016, at 11:54 PM by 130.130.136.114 -
Added lines 16-19:

*Algebraic characterization of periodic expansions

*Detection of linear dependence for the coordinates of the  vector to be expanded
Changed lines 6-9 from:
**Additive form
**Multiplicative form

to:
**Additive form, Multiplicative form

Changed lines 11-12 from:
to:
**Properties of transfer operator
Changed lines 14-15 from:
**Metric ones: Borel-Berstein type theorem
to:
**Lypunov exponents
**Metric number theory:
Borel-Berstein type theorem, Khinchine type theorem
Added lines 4-7:

*Description
**Additive form
**Multiplicative form
Changed lines 7-8 from:

to:
**Invariant measure, natural extension
Added lines 10-11:
**Metric ones: Borel-Berstein type theorem
Added lines 2-4:

Terminology: see the papers by T. Garrity

Changed lines 1-12 from:
!!!Toward a classification  of algorithms
to:
!!!Toward a classification  of continued fraction algorithms

*Ergodic properties


*Diophantine properties

*Applications

** Discrete geometry

**Addition chains
November 23, 2016, at 12:24 PM by 172.23.131.187 -
November 23, 2016, at 11:51 AM by 172.23.131.187 -
Changed line 1 from:
Toward a classification  of algorithms
to:
!!!Toward a classification  of algorithms
November 23, 2016, at 11:49 AM by 172.23.131.187 -
Added line 1:
Toward a classification  of algorithms