Holomorphic dynamical systems
and arithmetic
- Members- Research interests
- Activity
- Conferences
- Current research projects
- Recent publications
- Web page:
- Seminars:
- Visitors
Members:
Marco Abate, full professor, Pisa
Anna Miriam Benini, post doc, Centro di Ricerca Matematica "Ennio De Giorgi"
Filippo Bracci, full professor, Roma Tor Vergata
Carlo Carminati, assistant professor, Pisa
Stefano Marmi, full professor, Scuola Normale Superiore
Jasmin Raissy, post doc, Milano Bicocca
David Sauzin, full professor, Pisa
Francesca Tovena, associate professor, Roma Tor Vergata
Research interests:
Holomorphic dynamics in one and several complex variables, small divisor problems, continued fractions, measured foliations.
Activity:
Regular seminars on dynamical systems, Centro di Ricerca Matematica Ennio de Giorgi.
http://crm.sns.it/event/258/timetable.html
Conferences:
http://www.sns.it/ricerca/scienze/matematica/sistemidinamici/convegni/
Current research projects:
Dynamics of holomorphic maps in several complex variables in a neighborhood of a non-hyperbolic fixed point
Arithmetical conditions and solutions of cohomological equations for interval exchange maps
Ergodic theory and continued fractions
Recent publications:
[MMY] S. Marmi, P. Moussa and J. C. Yoccoz
Linearization of
generalized interval exchange maps, Accepted for publications on Annals of Mathematics Vol. 176, no. 3, 52 pages (2012)
[MTH] S. Marmi, P. Tempesta
Hyperfunctions, Formal Groups and Generalized Lipschitz Summation Formulas, Nonlinear Analysis, Theory, Methods and Applications, Volume 75, Issue 4, Pages 1768-1777 (2012)
[ABST] M. Abate, F. Bracci, T. Suwa, F. Tovena
Localization of Atiyah
Classes, Revista Matematica Iberoamericana, in stampa
[ABHK] L. Arosio, F. Bracci, H. Hamada, G. Kohr
An abstract approach to
Loewner's chains, J. Anal. Math, in stampa
[BC] F. Bracci, M. D. Contreras, S. Dìaz-Madrigal
Evolution Families and the Loewner Equation I: the unit disc, J. Reine Angew. Math., in stampa
[BZ] F. Bracci, D. Zaitsev
Dynamics of one-resonant biholomorphisms, J. Eur. Math. Soc., in stampa
M.Abate, F.Tovena
A Poincaré-Bendixson theorems for meromorphic connections and homogeneous fields, J. Diff. Equations, 251, 73 pages (2011)
[CMS] C. Carminati, S. Marmi and D. Sauzin
There is only one KAM curve, preprint arXiv:1104.2979, 33 pages (2011)
[CM] C. Chavaudret, S. Marmi
Reducibility of cocycles under a Brjuno-Rüssmann arithmetical condition, preprint arXiv:1107.4704, 23 pages (2011)
[BCDM] F. Bracci, M. D. Contreras, S. Dìaz-Madrigal
Semigroups versus
evolution families in the Loewner theory, J. Anal. Math, 115, 1, 273-292 (2011)
[AB] L. Arosio, F. Bracci
Infinitesimal generators and the Loewner
equation on complete hyperbolic manifolds, Anal. Math. Phys., 1, 4, 337-350
(2011)
[BES] F. Bracci, M. Elin, D. Shoikhet
Normal forms and linearization of holomorphic dilation type semigroups in several variables, J. Nonlinear Convex
Anal., 12, 1, 143-154 (2011)
[MS]S. Marmi, D. Sauzin
A quasianalyticity property for monogenic solutions of small divisor problems, Bulletin of the Brazilian Mathematical Society Volume 42, Number 1, 45-74, (2011)
[A] M. Abate
Discrete holomorphic local dynamical systems. To appear in "Holomorphic dynamical systems", G.Gentili, J. Guénot, G. Patrizio eds., Lect. Notes in Math., Springer, Berlin (2010)
[BCDM] F. Bracci, M. D. Contreras, S. Dìaz-Madrigal
Pluripotential theory,
semigroups and boundary behavior of infinitesimal generators in strongly convex domains, J. Eur. Math. Soc., 12, 1, 23-53 (2010)
[BGPC] F. Bracci, G. Gentili, P. Poggi-Corradini
Valiron's construction
in higher dimension, Revista Matematica Iberoamericana, 26, 1, 57-76 (2010)
[CT] C. Carminati, G. Tiozzo,
"A canonical thickening of Q and the dynamics of continued fractions",preprint arXiv:1004.3790v1 april 2010
[CNRR] T. Casavecchia, I. Nisoli, J. Raissy, M. Ruggiero
Local dynamics of singular holomorphic foliations, M. Abate ed., ETS, Pisa (2010)
[GM]A. Giorgilli, S. Marmi
Convergence radius in the Poincaré-Siegel problem, Discrete and Continuous Dynamical Systems Series S, 3, 4, 601-621 (2010)
[MNN]L. Luzzi, S. Marmi, H. Nakada and R. Natsui
Generalized Brjuno functions associated to \alpha-continued fractions, Journal of Approximation Theory, 162, n. 1, January, 24-41 (2010)
[MMY] S. Marmi, P. Moussa and J.-C. Yoccoz
Affine interval exchange maps with a wandering interval, Proceedings of the London Mathematical Society, 100(3): 639-669 (2010)
[CMPT] C. Carminati, S. Marmi, A. Profeti, G. Tiozzo,
The entropy of \alpha-continued fractions: numerical results, preprint arXiv:0912.2329v1 [math.DS] december 2009
[ABT] M. Abate, F. Bracci e F. Tovena
Embeddings of submanifolds and normal bundles. Adv. Math. 220, 620-656 (2009)
[BCDM] F. Bracci, M. D. Contreras, S. Dìaz-Madrigal
Evolution Families and the Loewner Equation II: complex hyperbolic manifolds, Math. Ann., 344, 4, 947-962 (2009)
[BPT] F. Bracci, G. Patrizio, S. Trapani
The pluricomplex Poisson
kernel for strongly convex domains, Trans. Amer. Math. Soc., 361, 2, 979-1005 (2009)
[BS] F. Bracci, A. Saracco
Hyperbolicity in unbounded convex domains, Forum Math., 21, 5, 815-826 (2009)
[DSM]J. De Simoi, S. Marmi
Potts models on hierarchical lattices and renormalization group dynamics, Journal of Physics A: Mathematical and Theoretical, 42, Number 9, 1-21 (2009)
[T] F.Tovena
A general approach to index theorems for holomorphic maps and foliations, Geometriae Dedicata, volume 139, 17 pages (2009)
[ABT] M. Abate, F. Bracci e F. Tovena
Index theorems for holomorphic maps and foliations. Indiana Univ. Math. J. 57, 2999-3048 (2008)
[AV] M. Abate, J.-P. Vigué
Isometries for the Carathéodory metric. Proc. Amer. Math. Soc. 136, 3905-3909 (2008)
[B] F. Bracci
A note on random holomorphic iteration in convex
Domains, Proc. Edinburgh Math. Soc., 51, 297-304 (2008)
[BZ] F. Bracci, D. Zaitsev
Boundary jets of holomorphic maps between strongly pseudoconvex domains, J. Funct. Anal., 254, 1449-1466 (2008)
[KM] D.H. Kim, S. Marmi
The recurrence time for interval exchange maps, Nonlinearity, 21, 2201-2210 (2008)
[LM]L. Luzzi, S. Marmi
On the entropy of japanese continued fractions, Discrete and Continuous Dynamical Systems A Volume 20, Number 3, 673-711, March 2008
[MK] S. Marmi, D.H. Kim,
The recurrence time for interval exchange maps,
Nonlinearity (2008)
[CM]C. Carminati, S. Marmi
Linearization of germs: regular dependence on the multiplier, Bull. Soc. Math. Fr. 136, p. 533-564 (2008)
[BCD] F. Bracci, M. D. Contreras, S. Dìaz-Madrigal
Classification of
semigroups of linear fractional maps in the unit ball, Adv. Math., 208, 318-350 (2007)
[BCD] F. Bracci, M. D. Contreras, S. Dìaz-Madrigal
Infinitesimal generators associated with semigroups of linear fractional maps, J. Anal. Math., 102, 119-142 (2007)
[BS] F. Bracci, B. Scàrdua
Holomorphic vector fields
transverse to polydiscs, J. London Math. Soc., 75, 1, 99-115 (2007)
[M]S. Marmi
From Small Divisors to Brjuno functions, Kokyuroku RIMS Kyoto 1493, no. 5, 1-47 (2006)
[MMY] S. Marmi, P. Moussa and J.-C. Yoccoz
The cohomological equation for Roth type interval exchange maps, J. Amer. Math. Soc 18, no. 4, 823-872 (2005)
[AB] M. Abate, F. Bracci
Ritt's theorem and the Heins map in hyperbolic complex manifolds. Science in China, Ser. A, 48 Suppl. , 238-243 (2005)
[AT] M. Abate, F. Tovena
Formal classification of holomorphic maps tangent to the identity. Disc. Cont. Dyn. Sys. Suppl. , 1-10 (2005)
[MMY] S. Marmi, P. Moussa and J.-C. Yoccoz
On the cohomological equation for interval exchange maps, C. R. Math. Acad. Sci. Paris 336, no. 11, 941-948 (2003)
[ABT] M. Abate, F. Bracci, F. Tovena
Index theorems for holomorphic self-maps. Ann. of Math. 159, 819-864 (2004)
[AT] M. Abate, F. Tovena
Parabolic curves in C^3. Abstr. Appl. Anal. , 275-294 (2003)
[MMY] S. Marmi, P. Moussa and J.-C. Yoccoz
On the cohomological equation for interval exchange maps', C. R. Math. Acad. Sci. Paris 336, no. 11, 941-948 (2003)
[MS] S. Marmi and D. Sauzin
Quasianalytic monogenic solutions of a cohomological equation, Memoirs of the American Mathematical Society 164, Number 780, 83 pages (2003)
[A] M. Abate
Basins of attraction in quadratic dynamical systems with a Jordan fixed point. Nonlinear Anal. 51, 271-282 (2002)
[HKMY] H. Eliasson, S. Kuksin, S. Marmi and J.C. Yoccoz
"Dynamical Systems and Small Divisors" Lecture Notes in Mathematics, 1784 Springer-Verlag (2002)
[MY] S. Marmi and J.-C. Yoccoz
"Some Open Problems Related To Small Divisors'', in Lecture Notes
in Mathematics 1784,pp. 175-191 (2002)
[MMY] S. Marmi, P. Moussa and J.C. Yoccoz
Complex Brjuno functions" Journal of the American Mathematical Society 14, pp. 783-841 (2001)
[A] M. Abate
"The residual index and the dynamics of holomorphic maps tangent to the identity" Duke Math. J. 107, 173-207 (2001)
[A] M. Abate
An introduction to hyperbolic dynamical systems. I.E.P.I. Pisa, 2001
[A] M. Abate
Diagonalization of non-diagonalizable discrete holomorphic dynamical systems. Amer. J. Math. 122, 757-781 (2000)
Web page:
http://www.sns.it/ricerca/scienze/matematica/sistemidinamici/
* Anno 2012 SEMINARI DI SISTEMI DINAMICI OLOMORFI
23-05-2012 - Complexity of geodesic flows on tori (Clémence Labrousse)
09-05-2012 - Remarks on the Moser normal form (Jacques Féjoz)
02-05-2012 - Rates of convergence in limit laws associated with infinite measure preserving transformations (Dalia Terhesiu)
21-03-2012 - The exactness of the Rauzy induction on the space of interval exchange transformations (Arnaldo Nogueira)
01-03-2012 - Dynamics of multi-resonant biholomorphisms (Jasmin Raissy)
23-02-2012 - Hausdorff dimension of biaccessible angles of quadratic Julia sets and of the Mandelbrot set (Henk Bruin)
15-02-2012 - Frontiere naturali forti secondo Breuer-Simon e funzione di suscettibilità di Ruelle (David Sauzin)
09-02-2012 - Polynomial entropies for integrable Hamiltonian systems (Jean-Pierre Marco)
26-01-2012 - The dimension set of recurrence of the irrational rotation (Kim, Dong Han)
19-01-2012 - On the Whitney-Holder differentiability of the SRB measure in the quadratic family (Viviane Baladi)
* Anno 2011 SEMINARI DI SISTEMI DINAMICI OLOMORFI
24-11-2011 - Absolute continuity of hitting measures for random walks (Giulio Tiozzo)
16-11-2011 - Reducibility of quasiperiodic linear systems under a Brjuno-Rüssmann arithmetical condition (Claire Chavaudret)
02-11-2011 - A transcendental separation theorem (Anna Miriam Benini)
08-06-2011 - Generic hyperbolic properties of classical systems on the torus \(T^2\) (Jean-Pierre Marco)
04-05-2011 - Ecalle-Voronin invariants and resurgent functions (Artem Dudko)
26-04-2011 - The Moduli Space of families of diffeomorphisms unfolding a parabolic point (Colin Christopher)
06-04-2011 - A codimension two manifold near a CR singular point (Wanke Yin)
26-04-2011 - Approssimazioni diofantee per le trasformazioni di scambio di intervalli, teorema di Khinchin e flusso di Teichmueller (Luca Marchese)
15-03-2011 - Metric inhomogeneous Diophantine approximation on the field of formal Laurent series (Kim, Dong Han)
10-01-2011 - From continued fractions to unimodal maps and back (Giulio Tiozzo)
* Anno 2010 SEMINARI DI SISTEMI DINAMICI OLOMORFI
22-06-2010 - (Attracting divisors on projective algebraic manifolds(Margaret Friedland)
11-06-2010 - (An "arithmetic microscope" for theta sums: continued fractions with even partial quotients(Francesco Cellarosi)
12-05-2010 - (On some universal aspects of the dynamics near invariant tori in Hamiltonian systems(Giampaolo Cristadoro)
12-05-2010 - (Central limit theorem for dimension of Gibbs measures in hyperbolic dynamics(Benoit Saussol)
05-05-2010 - (A canonical thickening of Q and the dynamics of continued fractions(Carlo CARMINATI)
20-01-2010 - (Almost reducibility of analytic quasi-periodic cocycles(Claire Chavaudret )
* Anno 2009: SEMINARI DI SISTEMI DINAMICI OLOMORFI
09-12-2009 - (Una Versione Non-Autonoma del Teorema di Denjoy-Wolff (Tiziano Casavecchia )
19-11-2009 - (Sulla classificazione dei germi semi-superattrattivi in C^2 (Matteo Ruggiero (SNS, Pisa) )
27-10-2009 - (Alcuni aspetti dinamici e PDE della teoria di Aubry-Mather-Mané(Olga Bernardi)
07-10-2009 - ( On mixing properties of area-preserving flows on surfaces(Prof. Corinna Ulcigrai)
07-05-2009 - ( Teoremi di Poincaré-Bendixson per connessioni meromorfe e campi vettoriali omogenei (II)(Marco Abate)
28-04-2009 - ( Teoremi di Poincaré-Bendixson per connessioni meromorfe e campi vettoriali omogenei (I)(Marco Abate)
17-03-2009 - (Moti a energia illimitata in un limite anti-integrabile della mappa standard(Dr. Jacopo De Simoi)
16-01-2009 - (Spectral analysis of the Perron-Frobenius operator for continued fractions(Giulio Tiozzo)
* Anno 2008: SEMINARI DI SISTEMI DINAMICI OLOMORFI
26-11-2008 - (A rigidity condition for holomorphic generators in strongly convex domains(Tiziano Casavecchia)
24-04-2008 - (Foliazioni olomorfe: Classificazione nel dominio di Siegel (3)(Matteo Ruggiero)
17-04-2008 - (Foliazioni olomorfe: Classificazione nel dominio di Siegel (2)(Matteo Ruggiero)
15-04-2008 - (Complexity of Hamiltonian systems and modern symplectic topology(Felix Schlenk)
09-04-2008 - (Foliazioni olomorfe: Classificazione nel dominio di Siegel (1)(Matteo Ruggiero)
08-04-2008 - (Minimal entropy and geometric decompositions(Pablo Suarez-Serrato)
27-03-2008 - (Foliazioni olomorfe: Classificazione nel dominio di Poincare' (3)(Jasmin Raissy)
20-03-2008 - (Foliazioni olomorfe: Classificazione nel dominio di Poincare' (2)(Jasmin Raissy)
28-02-2008 - (Famiglie di evoluzione su varietà iperboliche(Filippo BRACCI)
28-02-2008 - (Foliazioni olomorfe: il Teorema di Seidenberg (3)(Tiziano Casavecchia)
15-02-2008 - (Foliazioni olomorfe: il Teorema di Seidenberg (2)(Tiziano Casavecchia)
21-01-2008 - (Fourier Law And Random Walks In Dynamical Environment(Carlangelo Liverani)
2006
Nguyen Tien Zung (Universite' Paul Sabatier, Toulouse) February 27 - March 3
Jacky CRESSON (IHES Paris) April 3 - 10
Francesca Tovena (Univ. di Roma Tor Vergata) May 3 - 10
Pietro Poggi-Corradini (Kansas State University) May 29 - June 5
Corinna Ulcigrai (Università di Princeton) June19 - 25
Graziano Gentili (Universita' di Firenze) September 19 - 21
Hitoshi Nakada (Keio University) September 25 - 30
David Sauzin (IMCCE) November 14 - 20
Patrick Bernard (CNRS) November 20 - 25
Ugo Bessi (Università Roma 3) November 20 - 25
2005
Eugen MIHAILESCU (Institute of Mathematics of the Romanian Academy) November 8-12, 2004
Geon CHOE (Korea Advanced Institute of Science and Technology and Imperial College, London) November 22 - December 3, 2004
Gianluigi DEL MAGNO (Centro De Giorgi) December 15, 2004
Artur AVILA (CNRS, Parigi) January 24 - February 4, 2005
Viviane BALADI (CNRS, Institut Mathématique de Jussieu, Parigi) February 7-18, 2005
Albert FATHI (ENS Lyon) February 7-25, 2005
Nalini ANANTHARAMAN (E.N.S. Lyon) February 28 - March 4, 2005
Chiara FROSINI (Università di Firenze) March 22, 2005
Jean-Christophe YOCCOZ (Collège de France) March 28 - April 15, 2005
Pierre MOUSSA (CEA Saclay) March 28 - April 15, 2005
Jean-Rene CHAZOTTES (CPHT, CNRS-Ecole Polytechnique) April 12, 2005
Nuria FAGELLA (Universitat de Barcellona) April 26-29, 2005
Francesca TOVENA (Università di Roma Tor Vergata) 17 maggio 2005
2004
Pierre MOUSSA (CEA Saclay) January 19-30, 2004
Laura MOLINO (Università di Roma Tor Vergata) March 1-5, 2004
Joao LOPES-DIAS (Universidade Tecnica de Lisboa ) March 8-13, 2004
Bruno SCARDUA (IMPA) March 22-25, 2004
Francois BERTELOOT (Université Paul-Sabatier, Toulouse) March 29-31, 2004
Etienne GHYS (ENS Lyon) April 12-15, 2004
John HUBBARD (Cornell University) April 19-22, 2004
Marcelo VIANA (IMPA) April 26-30,
Jean-Yves BRIEND (Université de Marseille) May 3-6, 2004
Francesca TOVENA (Università di Roma Tor Vergata) May 31, 2004
2003
Francois BERTELOOT (one week at the end of April 2003)
Hakan ELIASSON (one week including April 10, 2003)
Jeff DILLER (May 12 - July 12, 2003) Albert FATHI (June 9-15, 2003)
Charles FAVRE (one week in March 2003)
Mattias JONSSON (April 21-27, 2003)
David SAUZIN (January 28-February 14 2003)
Nessim SIBONY (May 7-13, 2003)
Jean-Christophe YOCCOZ (one week in May 2003)
Anton ZORICH (one week in April 2003)
Todor V. GRAMTCHEV (December 16-19, 2003)