WORKSHOP ON PIECEWISE ISOMETRIES
Marseille- Luminy (IML)
June 2-15, 2002

sponsored by CNRS ,

FRUMAM , CPT , IML , and ESF .
logo

 

paradise

Piecewise Isometries are two and higher dimensional generalizations of well-known interval exchange transformations. Recent wide interest in the subject is partially driven by (a) analogies with one dimensional maps, (b) spectacular fractal mosaics of cells, as well as, (c) potential applications. These include other areas of mathematics such as dual billiards, Hamiltonian systems, as well as other areas of science: Electrical Engineering (Digital Filters) and Psychiatry.


The workshop will bring together researchers interested in the development of the theory of piecewise isometric maps and in related topics. Apart from research talks a series of introductory lectures will be delivered aimed at graduates students and nonexperts.


The workshop will be held in Luminy, one of the world centers for dynamical systems. The campus is located closed to Marseille and Callanques . Callanques are a unique natural sanctuary located at a spectacular 45--60 minute walk from campus to the Mediteranian sea. The old part of Marseille can be reached within 30-40 minutes by bus. Maps and directions are available from the CPT page. Also, directions to Luminy and to hotels are below.



 

Partial List of Participants.

02/6- 9/6
2/6- 15/6
9/6-16/6
30/5-30/6
5/6-?
2/6- 8/6
9/6-14/6
2/6- 9/6
4/6-5/6
2/6-14/6
6/4 -17/8

10/6-15/6
30/5 -?
29/5-?/6
30/5 -12/6
30/5 - 12/6
2/6 -9/6
2/6 - 15/6
2/6 - 14/6

?-?
1/6 -15/6
2/6 - 10/6
2/6 -9/6
2/6-10/6
2/6-9/6
2/6-16/6
2/6-13/6

17/5-17/6

9/6-15/6
30/5-10/7

Ashwin ( Exeter, GB)
Band (Warick)
Bis ( Lodz )
Boshernitzan (Rice)
Bremont (Paris)
Bruin ( Groningen)
Cheung (Northwestern)
Field (Houston)
Gambaudo (Dijon)
Genin ( State College)
Goetz (SFSU)
Gutkin (IHES)
Haydn (USC)
Holton ( Berkeley)
Hu ( Los Angeles)
Kahng (W&M, Virginia) Kosek ( Lille)
Lanneau (Rennes )
Lelievre (Rennes )

Lopez (CIMAT)
Lowenstein (New York)
Melbourne (Surrey)
Mendes (Surrey)
Misiurewicz (IUPUI)
Nicol (Surrey)
Rams (Warsaw)
Sammis (SFSU)
Tabachnikov (S. College) F. Vivaldi (London)
 Zamboni (Denton,TX )


Local Participants:

A. Aberkane,
B. Adamczewski,
P. Arnoux,
N. Bedaride ,
V. Berthe,
F. Blanchard,

X. Bressaud,
J. Cassaigne,

S. Ferenczi, (first week)
B.Fernandez,
P. Hubert,
J. Los,
G. Poggiaspalla,
S. Ruette,
S. Troubetzkoy,
S. Vaienti.

 

Organizer : S. Troubetzkoy (IML-CPT),


Scientific committee : P. Ashwin (University of Exeter), M. Boshernitzan (Rice University), N. Haydn (University of Southern California), F. Przytycki (Polish Academy of Sciences and Warsaw University).

Organizing committee : X. Bressaud (IML), J. Cassaigne (IML), S. Ferenczi (IML), A. Goetz (San Francisco State University), P. Hubert (IML), G. Poggiaspalla ( CPT-Universite Aix Marseille II),
S. Troubetzkoy (IML-CPT), S. Vaienti (CPT et Universite de Toulon et du Var).

Local organizing committee : X. Bressaud (IML), P. Hubert (IML), S. Troubetzkoy (IML-CPT), S. Vaienti (CPT, Universitte de Toulon et du Var).


Secretary : J. Brohan (IML), brohan@iml.univ-mrs.fr



conference building

conference building 

Address: Institut de Mathematiques de Luminy,Luminy Case 907
F-13288 Marseille Cedex 09, France




Tentative Schedule:

All talks will be in the building pictured above. the buildings contains among others, CPT and IML. Access to the building is via the security reception. The talks will be held in  room 210 (Serge's office is 207 and J. Brohan's office is  311.
Minicourses:

Week 1

Sebastien Ferenczi, Unique ergodicity of interval exchanges, a symbolic proof. We explain a proof due to M. Boshernitzan of the famous Veech-Masur result, that almost all interval exchange transformations are uniquely ergodic . Thisuses only elementary tools such as complexity function and graph of words, and might be useful to understand more general piecewise isometries .

Arek Goetz , Dynamics of Piecewise Isometries, from introductory examples to current research questions. The series will start off from the introduction to the subject accessible to non experts and then it will quickly move to a survey of theory and research tools. While preserving the mathematical rigor, the series will be augmented by frequent interactive computer illustrations and animations.

Week 2

Michael Boshernitzan Combinatorial and Diophantine properties of Interval Exchange Transformations.

Franco Vivaldi Arithmetic dynamics of some linear and piecewise linear maps .

Week 1:

Monday

Tuesday

Wednesday

Thursday

Friday

Time

Goetz
Dynamics of Piecewise Isometries, from introductory examples to current research questions.

Ferenczi Unique ergodicity of interval exchanges, a symbolic proof .

Poggiaspalla

Rotations by pi/7 (40 min)

Mendes
The definition of attractor and examples arising in the Goetz map. (40 min)

 

 

 

Goetz Dynamics of Piecewise Isometries, from introductory examples to current research questions.

Ferenczi Unique ergodicity of interval exchanges, a symbolic proof .

10:00-11:30

Zamboni

Maximum pattern complexity of discrete dynamical systems

 

Nicol
Some results on piecewise isometries in dimensions n>2.

Field

Stability of ergodicity and transitivity for compact group extensionsof hyperbolic sets.

Misiurewicz

Area preserving attractors.

 

Bruin

Gauss map on a certain space of i.t.m.

11:30-12:30

lunch

lunch

lunch

lunch

lunch

12:30-2:30

Ashwin

The geometry of orientation-preserving piecewise isometries

Gambaudo

Tilings and laminations

Hike to the beaches and callanques.

Meeting at 2:30 p.m . under the

 

 

coffee break (3:00-3:30)

Cassaigne

Complexity of some i.t.m.

2:30-3:30

coffee break

coffee break

University cafeteria.

Hubbard
TBA

 

coffee break


3:30-4:30

 

 

TAKE LOTS OF WATER,

Callanques can be very dangerous.

 

 

picnic
(7:30 p.m.),
great food and drinks in a beautiful sourandings

 

 

On Saturday and Sunday we suggest that the participants enjoy private and professional conversation and explore nature adn the city. Local organizers will be more than happy to suggest some beautiful walks boat rides, or dinner places.

Week 2:

Monday

Tuesday

Wednesday

Thursday

Friday

Time

Boshernitzan

Combinatorial and Diophantine properties of Interval Exchange Transformations.

Vivaldi

Arithmetic dynamics of some linear and piecewise linear maps

Sammis
(40 min) pi/7 ---------------

Bedaride : Billiard complexity in the cube.
(40 min)

 

Vivaldi

Arithmetic dynamics of some linear and piecewise linear maps

Boshernitzan

Combinatorial and Diophantine properties of Interval Exchange Transformations.

 

10-11:30 a.m.

Julien Bremont

Rotation piecewise linearly contracting

Gutkin Periodicity and related questions for piecewise isometries

 

Bis
Dynamics of distributions

 

Lowenstein
Quadratic rational rotations of the torus and dual lattice
maps.

Band
Non-injectivity of Fathi'ssemiconjugacy
(40 min)

11:30-12:30 a.m.

lunch

lunch

lunch

lunch

lunch

 

12:30-2:30

Kahng
The invariant fractals of symplectic piecewise affine elliptic dynamics

Cheung

Hausdorff dimension, billiards and divergent trajectories

Hike to the beaches and callanques.

 

Tabachnikov
Polygonal outer billiards in the hyperbolic plane

 

Hubert

Interval translation mappings, invariant measures and topological model.

 

2:30-3:30

coffee break

 

coffee break

 

TAKE LOTS OF WATER,

Callanques can be very dangerous.

 

 

coffee break

 

 

3:30-4:30

 

 

 

 

picnic
(7:30 p.m.),
great food and drinks in a beautiful sourandings

 

 

 


Reaching Luminy

If you happen to need urgent advice, please call Arek Goetz on his French cell phone, 06.77.87.26.74.

While many visitors to Luminy now choose to fly to Paris and then take a convenient fast train (the trip takes slightly more than three hours) from the airport CDG in Paris , the instructions below include an option when a visitor arrives in Marseille by plane or by train.

If you arrive in Marseille by plane, use the shuttle bus from the airport to the city center that runs every 20 minutes. A ticket costs 7 ,60EUR.Get off the bus at the final stop, at the main railway station ( St Charles ). From the station, until 21:00, take metro line 2 towards Ste Marguerite- Dromel.Get off one stop before the end of the line, at Rond-Point duPrado , then take bus 21 towards Luminy to its last stop.The The bus stop is on the other side of the avenue.On Sundays, all busses of the line run to Luminy; on weekdays, avoid busses marked " Valmante " that do not go all the way.The metro ticket 1,40 EUR is also valid on the bus, you do not need to buy a new one.

After 21:00, the metro does not run any more, but there is a direct bus from the railway station to Luminy: line 521, departing from St Charles at 21:19, 21:54, 22:34, 23:09, 23:49 and 00:24 . At night please be aware of groups of young men trying to steal money and cell phones on the bus and near the bus stops.

To reach the 521 bus stop (after 21:00) from the railway station, follow the signs "garerouti?re " and exit the station on the side opposite to the airport shuttle, near track M.Then take the street (rue Honnorat ) to the left, then turn right along the fence.

For further information about public transportation in Marseille: http://www.lepilote.com/

Of course, you can also come by taxi.By day the fare should be around 55 EUR from the airport and 20 EUR from the station.


REACHING HOTELS

Important: If you plan to arrive in your hotel after 6 p.m., please call the reception and ask how you can obtain the key to your room.

The directions below were composed by local faculty who know the town. It is best however, to also print hyperlinked maps to the hotels.

From Saint-Charles railway station to Etape Hotel,  46 Rue Sainte, 04 91 54 73 73. Take subway line 1, direction La Timone , get off at Vieux Port , the hotel is a 5 minutes walk. Rue Sainte is the 2nd street parallel to the (left if facing from the top) bank of the Vieux Port.

From the train station to Hotel President, 12 BdSalvator 04 91 48 67 29.

By foot: Descend the grand staircase of the station (stone staircase, construction of the beginning of the 20th century). Walk straight for approximately 15 to 20 minutes.One crosses many small streets, but only one large street one crosses is called la Canebiere . The street which one follows changes its many several times, but after approximately 5 minutes is is called coursLieutaud . On passes under 2 bridges.Boulevard Salvator is the 2 nd street on the right after the second bridge.This is a steeply descending street, with trees.The hotel is at the bottom of the street.

By metro: Take line 2 in the direction: Sainte Marguerite Dromel. Exit atthe station: Notre Dame du Mont, Cours Julien. Take the exit labeled : Cours Julien. At the top of the escalator continue to walk in the direction of the exit. You will arrive at a long square place Notre Dame duMont.Cross this diagonally.At the other end of the square the church Notre Dame du Mont will be on your left.Take the rue des Berger which slopes down on your right.Cross cours Lieutaud.The boulevard Salvator is the continuation of the rue Berger. The hotel is at the bottom of the street.

Directions from the trains station to CITADINES PRADO-CHANOT , 9/11 boulevard de Louvain , 13008 Marseille, Tel. : 08 25 01 03 68. Take the metro, line 2 in the direction: Sainte Marguerite Dromel . Exit at the station Perrier or Rond Point de Prado. Walk along Ave du Prado until you reach bloulevard de Louvain, (it is half way between the two stops on your left if you are coming from Perrier and on your right if you are coming from the Rond Point.) The hotel is approximately 150 meters on your left (opposite the main entrance to the hospital Ste Joseph).

From Saint-Charles railway station to Luminy : Take subway line 2, direction Dromel Ste Marguerite, get off at Rond Point du Prado,then , take the Bus21 to the terminus.

From Etape Hotel to Luminy : Walk to Vieux Port , take subwayline 1directionLa Timone, get off at Castellane and take the Bus 21, direction Luminy to the terminus.

The subway runs from 5.00a.m. to 9.00p.m.

How to reach hotel Montgrand (50 rue Montgrand) from the train station.
By foot
: Descend the grand staircase of the station (stone staircase, construction of the beginning of the 20th century). Walk straight for approximately 5 minutes until you reach la Canabiere , a large street which descends to the Vieux Port (one crosses several small streets before and the street which one follows changes its many several times). Turn right on la Canebier, cross to the far side and descend to rue St. Fereol . Turn left on this street and after several blocks turn right on rue Montgrand .

By metro: take line 1 direction : Timone. Exit at the station: Estrangin-Pr\'efecture . At the exist of the station take rue Paradis in the direction where the house numbers decrease.RueMontgrand is the 2nd street, turn left into this street.The hotel is close.