CRM: Centro De Giorgi
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Holomorphic dynamical systems and arithmetic



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/

Seminars