Marseille-Luminy (IML)
June 2-15, 2002

sponsored by CNRS , FRUMAM , CPT and  IML

(updated: April, 2002)


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.



Partial List of Participants.
(*) indicates no commitment

Dates or arrival and departure are approximate.

02/6- 9/6



2/6- 8/6



2/6- 9/6









2/6 -14/6  

2/6 -14/6  




2/6 -9/6    

29/5 -10/6

2/6 - 10/6 

2/6 - 9/6  

2/6 - 9/6    

2/6 -13/6  

2/6 - 13/6  

14/5 -14/6

9/6 - 15/6  



P. Ashwin (Exeter, GB)
M. Boshernitzan (Rice, Houston)-J. Buzzi(*)
H. Bruin (
Y. Cheung (Northwestern)

A. Eskin (*)
M. Field (Houston)
D. Gaboriau (*)
J. Gambaudo (several days)
D. Genin (State College)
A. Goetz (SFSU,San Francisco)
N. Haydn (USC,Los Angeles)
C. Holton (Berkeley)
H. Hu (Los Angeles)
B. Kahng (W&M, Virginia)
E. Lanneau (Rennes)
S. Lelievre (Rennes)
G. Levitt (*)
J. Lowenstein (New York)
H. Masur (*)
I. Melbourne
M. Mendes (Surrey)
M. Misiurewicz (IUPUI, Indiana)
M. Nicol (Surrey)
F. Przytycki (Warsaw)
M. Rams (Warsaw)
I. Sammis (SFSU, San Francisco)
S. Tabachnikov (S. College)
F. Vivaldi (London)
A. Zorich (*)
L. 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)
P. Hubert,
J. Los,
G. Poggiaspalla,
S. Ruette,
S. Troubetzkoy,
S. Vaienti.



Organizer : S. Troubetzkoy (IML-CPT), or

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),

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


Tentative Schedule:


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. This  uses 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 TBA,TBA,TBA

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

Talks: Detailed schedule of talks will be posted here
within two weeks or so. Talks will last between 40 minutes and one hour each.
























Reaching Luminy

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

While many visitors to Luminy now choose to fly to Paris and then take a convenient fast train (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 and 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 7,60 EUR.  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 du Prado, 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.

To reach the 521 bus stop (after 21:00) from the railway  station, follow the signs "gare routičre" 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:

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.

From Saint-Charles railway station to Etape Hotel: 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 Bd Salvator 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 cours Lieutaud. On passes under 2 bridges.  Boulevard Salvator is the 2nd 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 at the 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 du Mont.  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 Bus  21 to the terminus.

From Etape Hotel to Luminy : Walk to Vieux Port, take  subway  line 1  direction  La 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.