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WORKSHOP ON PIECEWISE ISOMETRIES
Marseille- Luminy (IML)
June 2-15, 2002
sponsored by CNRS ,
FRUMAM , CPT , IML ,
and ESF .
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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.
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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
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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 )
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Local Participants:
A. Aberkane,
B. Adamczewski,
P. Arnoux,
N. Bedaride ,
V. Berthe,
F. Blanchard,
X. Bressaud,
J. Cassaigne,
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S. Ferenczi, (first
week)
B.Fernandez,
P. Hubert,
J. Los,
G. Poggiaspalla,
S. Ruette,
S. Troubetzkoy,
S. Vaienti.
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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
Address: Institut de Mathematiques de Luminy,Luminy Case
907
F-13288 Marseille Cedex 09, France
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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:
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Goetz
Dynamics of Piecewise Isometries, from introductory examples to current
research questions.
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Ferenczi Unique ergodicity of interval exchanges, a
symbolic proof .
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Poggiaspalla
Rotations by pi/7 (40 min)
Mendes
The definition of attractor and examples arising in the Goetz map.
(40 min)
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Goetz Dynamics
of Piecewise Isometries, from introductory examples to current research
questions.
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Ferenczi Unique ergodicity of interval exchanges, a
symbolic proof .
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Zamboni
Maximum pattern complexity of discrete dynamical
systems
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Nicol
Some results on piecewise isometries in dimensions n>2.
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Field
Stability of
ergodicity and transitivity for compact group extensionsof hyperbolic sets.
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Misiurewicz
Area preserving attractors.
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Bruin
Gauss map on a certain space of i.t.m.
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lunch
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lunch
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lunch
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lunch
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lunch
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12:30-2:30
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Ashwin
The geometry of
orientation-preserving piecewise isometries
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Gambaudo
Tilings and laminations
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Hike to the beaches and callanques.
Meeting at 2:30
p.m . under the
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Cassaigne
Complexity of some i.t.m.
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coffee break
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coffee break
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University cafeteria.
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Hubbard
TBA
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coffee break
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3:30-4:30
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TAKE LOTS OF WATER,
Callanques can be very
dangerous.
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picnic
(7:30 p.m.),
great food and drinks in a beautiful sourandings
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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:
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Boshernitzan
Combinatorial and
Diophantine properties of Interval Exchange Transformations.
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Vivaldi
Arithmetic dynamics of some linear and piecewise
linear maps
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Sammis
(40 min) pi/7 ---------------
Bedaride : Billiard complexity in the cube.
(40 min)
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Vivaldi
Arithmetic dynamics of some linear and piecewise
linear maps
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Boshernitzan
Combinatorial and
Diophantine properties of Interval Exchange Transformations.
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Julien Bremont
Rotation piecewise linearly contracting
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Gutkin Periodicity
and related questions for piecewise isometries
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Bis
Dynamics of distributions
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Lowenstein
Quadratic rational rotations of the torus
and dual lattice
maps.
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Band
Non-injectivity of Fathi'ssemiconjugacy
(40 min)
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lunch
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lunch
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lunch
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lunch
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lunch
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12:30-2:30
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Kahng
The invariant fractals of symplectic piecewise affine elliptic dynamics
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Cheung
Hausdorff dimension, billiards and divergent
trajectories
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Hike to the beaches and callanques.
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Tabachnikov
Polygonal outer billiards in the hyperbolic plane
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Hubert
Interval translation mappings, invariant measures
and topological model.
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2:30-3:30
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coffee break
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coffee break
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TAKE LOTS OF WATER,
Callanques can be very
dangerous.
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coffee break
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3:30-4:30
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picnic
(7:30 p.m.),
great food and drinks in a beautiful sourandings
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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.
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