Luigi Chierchia

Professor of mathematical analysis

114829 Chierchia (2003 OC21)

E-mail: luigi@mat.uniroma3.it
Phone: +39-0657338235, +39-0657338212
Fax: +39-0657338072, +39-0657338080
Address: Dipartimento di Matematica, Università Roma Tre, Largo San L. Murialdo 1, I-00146 ROMA - Italy
Studio (Office): stanza n. 210, piano 2 (2nd Floor), Edificio (Building) C

Some recent Conferences

Students (Master/PhD)

*Formation:*	Master ("laurea"), University of Roma "La Sapienza" (1981) Ph. D., Courant Institute, NYU (1985) Post doc: University of Arizona, ETH (Zürich), École Polytechnique (Palaiseau)
*Main scientific interests:*	Nonlinear differential equations and dynamical systems with emphasis on stability problems in Hamiltonian systems
*Other:*	Prix 1995 Institut Henri Poincaré the papers Drift and diffusion in phase space and A direct proof of a theorem by Kolmogorov in Hamiltonian systems have been selected by the AMS for the volume "FEATURED REVIEWS in Math Rev 1995-96. Reviews of Outstanding Recent Books and Papers, American Mathematical Society 1997". Director of the local unit Roma TRE for the "PRIN" project (MURST/ MIUR ) Variational methods and nonlinear differential equations (1998-1999, 2000-2001, 2002-2003, 2004-2005, 2006-2007) Roma Conference (January 10-14, 2005) Member of the scientific committee for the conferences: Dynamics, topology and computations (Bedlewo, Poland, May 31- June 6, 2009) Hamiltonian Systems - Special Session at the Poitiers AIMS Conference (Poitiers, France, June 25-28, 2006) Dynamics, topology and computations (Bedlewo, Poland, June 4-10, 2006) Regular and unstable motions in Hamiltonian systems , Roma Sept. 6-9, 2000 invited lecturer in about 40 international conferences

Preprints

Properly-degenerate KAM theory (following V.I. Arnold) , Oct. 7, 2009
(with G. Pinzari. To appear in DCDS-S)

Kolmogorov-Arnold-Moser theory , Scholarpedia (the free peer reviewed web encyclopedia), 2009

Publications

(For reprints send an e-mail to luigi@mat.uniroma3.it )

Papers:

Kolmogorov-Arnold-Moser (KAM) Theory
in: Encyclopedia of Complexity and Systems Science. Editor-in-chief: Meyers, Robert A
Version: print (book) 2009, DCCCLXXXII, 10398 p. 4540 illus., 2040 in color. In 11 volumes, not available separately. Hardcover
ISBN: 978-0-387-75888-6

Low-order resonances in weakly dissipative spin-orbit models
(with L. Biasco)
Journal of Diff. Equations, 246, 4345-4370 (2009)
doi:10.1016/j.jde.2008.11.008

Meeting Jürgen Moser
Regular and Chaotic Dynamics, 14, No. 1, 5-6 (2009)

Quasi-periodic attractors in celestial mechanics
(with A. Celletti)
Arch. Rational Mech. Anal., 191, Issue 2, 311-345 (2009)

Analytic Lagrangian tori for the planetary many-body problem
(with F. Pusateri)
Ergod. Th. & Dynam. Sys., 29, 3, Jun 2009, 849-873
doi:10.1017/S0143385708000503

Measures of Basins of Attraction in Spin-orbit Dynamics
(with A. Celletti)
Celest. Mech. Dyn. Astr. 101, 159-170 (2008)

A. N. Kolmogorov's 1954 paper on nearly-integrable Hamiltonian systems.
Regular and Chaotic Dynamics, Vol. 13, no. 2, pp. 130-139 (2008)

KAM theory and Celestial Mechanics
Encyclopedia of Mathematical Physics, eds. J.-P. Françoise, G.L. Naber and Tsou S.T.
Oxford: Elsevier, 2006, vol. 3, pp. 189-199
ISBN 978-0-1251-2666-3
(preprint, 24 p., January 2005)

KAM tori for N-body problems (a brief history)
(with A. Celletti)
Celestial Mechanics & Dynamical Astronomy, 95 , 2006 117-139
doi:10.1007/s10569-005-6215-x

N-dimensional elliptic invariant tori for the planar (N+1)-body problem
(with L. Biasco and E. Valdinoci)
SIAM Journal on Mathematical Analysis, 37 , Number 5, (2006) 1560-1588

Corrigendum to: Elliptic two-dimensional invariant tori for the planetary three-body problem
(with L. Biasco and E. Valdinoci)
Arch. Rational Mech. Anal., 180 , Number 3, (2006) 507-509
doi:10.1007/s00205-005-0410-5

Stability of nearly-integrable, degenerate Hamiltonian systems with two degrees of freedom
(with L. Biasco and D. Treschev)
J. Nonlinear Sci. Vol. 16 , pp. 79-107 (2006)
doi:10.1007/s00332-005-0692-7

KAM stability for a three-body problem of the Solar system
(with A. Celletti)
ZAMP (Zeitschrift für Angewandte Mathematik und Physik), 57 , Number 1, (2005) 33-41.

Exponential stability for the resonant D'Alembert model of Celestial Mechanics
(with L. Biasco)
Discrete Contin. Dyn. Syst. A, 12 , Number 4, 569-594 (2005)
Remarks and Typos (May 2007)

Moser's theorem for lower dimensional tori
(with D. Qian)
Journal of Diff. Equations, 206 (2004) 55-93

Elliptic two-dimensional invariant tori for the planetary three-body problem
(with L. Biasco and E. Valdinoci)
Arch. Rational Mech. Anal., 170, 91-135 (2003)

On the stability of some Properly degenerate Hamiltonian systems with two degrees of freedom
(with L. Biasco)
Discrete Contin. Dyn. Syst. A, 9, n. 2, 233-262 (2003)

Nekhoroshev stability for the D'Alembert problem of Celestial Mechanics
(with L. Biasco)
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 13, no. 2, 85-89 (2002)

Effective Hamiltonian for the D'Alembert Planetary model near a spin/orbit Resonance
(with L. Biasco)
Celestial Mechanics & Dynamical Astronomy, 83, 223-237 (2002)

Upper bounds on Arnold diffusion times via Mather theory
(with U. Bessi and E. Valdinoci)
J. Math. Pures Appl. 80, 1, 105-129 (2001)

Hamiltonian stability of spin-orbit resonances in Celestial Mechanics
(with A. Celletti)
Celestial Mechanics & Dynamical Astronomy, 76, 229-240 (2000)

KAM Tori for 1D Nonlinear Wave Equations with Periodic Boundary Conditions
(with J. You)
Commun. Math. Phys. 211, 497-525 (2000)

A note on the construction of Hamiltonian trajectories along heteroclinic chains
(with E. Valdinoci)
Forum Math, n. 12, p.247-255 (Feb. 2000)

Construction of stable periodic orbits for the Spin-Orbit problem of Celestial Mechanics
(with A. Celletti)
Regular and Chaotic Dynamics, Vol. 3, no. 3, 107-121 (1998)

KAM stability estimates in Celestial Mechanics
(with A. Celletti)
Planet. Space Sci., 46, no. 11/12, 1433-1440 (1998)

On the stability of realistic three-body problems,
(with A. Celletti)
Commun. Math. Phys., 186, 413-449 (1997)

A note on Quasi-periodic solutions of some elliptic systems
(with C. Falcolini)
ZAMP, (Zeitschrift für Angewandte Mathematik und Physik), 47, 210-220 (1996)

Compensations in small divisor problems
(with C. Falcolini)
Commun. Math. Phys., 175, 135-160 (1996)

Second order Hamiltonian equations on T^∞ and almost-periodic solutions
(with P. Perfetti)
Journal of Diff. Equations, 116, No. 1, 172-201 (1995)

A Direct Proof of a Theorem by Kolmogorov in Hamiltonian Systems
(with C. Falcolini)
Annali Scuola Normale Sup. Pisa, Scienze Fisiche e Matematiche, XXI Fasc. 4, 541-593 (1994)

Drift and diffusion in phase space
(with G. Gallavotti)
Ann. Inst. Henri Poincaré, Phys. Théor., 60, 1-144 (1994)
Erratum, Ann. Inst. Henri Poincaré, Phys. Théor., 68, no. 1, 135 (1998)

Natural boundaries for area-preserving twist maps
(with A. Berretti, A. Celletti and C. Falcolini)
Journal of Statistical Physics, 66, 1613-1630 (1992)

Invariant curves for area-preserving twist maps far from integrable
(with A. Celletti)
Journal of Statistical Physics, 65, 617-643 (1991)

On a result by J.N. Mather concerning invariant sets for area-preserving twist maps
ZAMP, (Zeitschrift für Angewandte Mathematik und Physik), 42, 80-89 (1991)

A direct method for the construction of solutions of the Hamilton-Jacobi equation
Meccanica, Journal of the Italian Association of Theoretical and Applied Mechanics, 25, 246-252 (1990)

On the complex analytic structure of the golden-mean invariant curve for the standard map
(with A. Berretti)
Nonlinearity, 3, 39-44 (1990)

Asymptotic expansions of quasi-periodic solutions
(with E. Zehnder)
Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4), XVI, 245-258 (1989)

Exponential estimates on the one-dimensional Schrödinger equation with bounded analytic potential
(with G. Benettin and F. Fassò)
Ann. Inst. Henri Poincaré, Phys. Théor., 51, 45-66 (1989)

Construction of analytic KAM surfaces and effective stability bounds
(with A. Celletti)
Commun. Math. Phys., 118, 119-161 (1988)

On rigorous stability results for low-dimensional KAM surfaces
(with A. Celletti)
Physics Letters A, 128, 166-168 (1988)

On the weak limit of rapidly oscillating waves
(with N. Ercolani and D. McLaughlin)
Duke Math. Journal, 55,759-764 (1987)

Absolutely continuous spectra of quasiperiodic Schrödinger operators
Journal of Math. Physics, 28, 2891-2898 (1987)

Rigorous estimates for a computer-assisted KAM theory
(with A. Celletti)
Journal of Math. Physics, 28, 2078-2086 (1987)

Smooth prime integrals for quasi-integrable Hamiltonian systems
(with G. Gallavotti)
Il Nuovo Cimento, 67 B, 277-295 (1982)

Books:

KAM stability and Celestial Mechanics

(with A. Celletti)
Memoirs of the AMS, Vol. 187, Number 878, (2007)
( preprint , 127 p., Dec. 2003)

KAM lectures PDF
in "Dynamical Systems. Part I: Hamiltonian Systems and Celestial Mechanics",
Pubblicazioni della Classe di Scienze, Scuola Normale Superiore, Pisa. Pagg. 1-56. Centro di Ricerca Matematica "Ennio De Giorgi": Proceedings (2003)

A constructive theory of Lagrangian tori and computer-assisted applications
(with A. Celletti)
Dynamics reported, 60-130, Dynam. Report. Expositions Dynam. Systems (N.S.), 4, Springer, Berlin, 1995

Quasi-periodic Schrödinger operators in one dimension, Absolutely continuous spectra, Bloch waves and integrable Hamiltonian systems
Quaderni del Consiglio Nazionale delle Ricerche, (Firenze, Italia), 127 pp. (1986)

Proceedings:

Quasi-periodic attractors and spin/orbit resonances
(with A. Celletti)
in SYMMETRY AND PERTURBATION THEORY, Proceedings of the International Conference on SPT 2007 Otranto, Italy 2 - 9 June 2007, edited by G. Gaeta, R. Vitolo & S. Walcher, Ed. World Scientific (2008)

On the convergence of formal series containig small divisors
(with C. Falcolini)
in "Hamiltonian systems with three or more degrees of freedom", NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. à S'Agaró, Espagne, 1995, (1999)

Arnold Instability for nearly-integrable Hamiltonian systems
in "Variational and Local Methods in the study of Hamiltonian systems", (Trieste, 1994), 17-33, World Sci. Publishing, pag. 17-33 (1995)

Maximal almost-periodic solutions for Lagrangian equations on infinite dimensional tori
(with P. Perfetti)
in "Seminar on Dynamical Systems" (St. Petersburg, 1991), 203-212, Progr. Nonlinear Differential Equations Appl., 12, Birkhäuser, Basel (1994)

On the stability problem for nearly-integrable Hamiltonian systems
in "Seminar on Dynamical Systems" (St. Petersburg, 1991), 35-46, Progr. Nonlinear Differential Equations Appl., 12, Birkhäuser, Basel (1994)

Birth and death of invariant tori for Hamiltonian systems
in "The geometry of Hamiltonian systems" (Berkeley, CA, 1989), 73-80, Math. Sci. Res. Inst. Publ., 22, Springer, New York, USA (1991)

A computer-assisted approach to small-divisors problems arising in Hamiltonian mechanics
(with A. Celletti)
in "Computer aided proofs in analysis" (Cincinnati, OH, 1989), 43-51, IMA Vol. Math. Appl., 28, Springer, New York (1991)

An effective theory of KAM surfaces
in "Nonlinear dynamics" (Bologna, 1988), 191-199, World Sci. Publishing, USA (1989)

A report on some new KAM estimates
(with A. Celletti)
in A.E. Roy (ed.), "Long-Term Dynamical Behaviour of Natural and Artificial N-body Systems", (Cortina d'Ampezzo, 1987)
371-375, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 246, Kluwer Acad. Publ., Dordrecht (1988)

Some recent Conferences

Classical and weak KAM theorem Montegrotto Terme (Italy), February 14-19, 2010

CELMEC V. The Fifth International Meeting on Celestial Mechanics San Martino al Cimino, Viterbo (Italy), September 6-12, 2009

DYNAMICS, TOPOLOGY AND COMPUTATIONS Bewdlewo (Poland), MAY 31 - JUNE 6, 2009

New connections between dynamical systems and Hamiltonian PDEs Maiori (Italy) June 1-6, 2009

KAM Theory and its applications Lorentz Center (Leiden) Dec 1-5 Dec 5, 2008

Conference on Stability and Instability in Mechanical Systems: Recent Progress and Mathematical Theory (Conferences & Workshops -> LIST OF PAST EVENTS -> Academic Year 2008-2009) CRM (Bellaterra) September 22-26, 2008

Workshop on Variational methods and Nash-Moser PIM (UBC, Vancouver) June 16-22, 2008

Workshop on Mathematical Aspects of Celestial Mechanics, Paris, Institut Henri Poincaré Institut Henri Poincaré (Paris) December 11-20, 2007

SPT 2007 Symmetry and Perturbation Theory Otranto (Italy) June 2-9, 2007

cedya 2007 SESSION 1: Dynamical systems and celestial mechanics, (Sevilla) September 24-28, 2007

2006 Nanjing Conference on Hamiltonian Dynamics (Nanjing) June 19-23, 2006

Some links

Assegni di Ricerca (ROMA TRE fellowships)

SIMCA (Società Italiana di Meccanica Celeste)