Guido Gentile

Publications

1. Published or accepted papers

1. G. Gentile, B. Scoppola
   Renormalization group and the ultraviolet problem in the Luttinger liquid
   Communications in Mathematical Physics 154 (1993), no. 1, 135-179. [MR1220952 (95a:81177)].

2. G. Gallavotti, G. Gentile
   Majorant series convergence for twistless KAM tori
   Ergodic Theory and Dynamical Systems 15 (1995), no. 5, 857-869. [MR1356618 (96h:58152)].

3. G. Gentile
   A proof of existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems
   Forum Mathematicum 7 (1995), no. 6, 709-753. [MR1359423 (97a:58164b)].

4. G. Gentile
   Whiskered tori with prefixed frequencies and Lyapunov spectrum
   Dynamics and Stability of Systems 10 (1995), no. 3, 269-308. [MR1356323 (97a:58164a)].

5. G. Gallavotti, G. Gentile, V. Mastropietro
   Field Theory and KAM tori
   Mathematical Physics Electronic Journal 1 (1995), Paper 5, pp. 13 (electronic). [MR1359460 (97b:81072)].

6. G. Gentile, V. Mastropietro
   Tree expansion and multiscale analysis for KAM tori
   Nonlinearity 8 (1995), no. 6, 1159-1178. [MR1363405 (97c:58137)].

7. G. Gentile, V. Mastropietro
   KAM theorem revisited
   Physica D 90 (1996), no. 3, 225-234. [MR1372451 (96k:58194)].

8. G. Gentile, V. Mastropietro
   Methods of analysis of the Lindstedt series for KAM tori and renormalizability in classical mechanics. A review with some applications
   Reviews in Mathematical Physics 8 (1996), no. 3, 393-444. [MR1388257 (98f:58169)].

9. G. Benfatto, G. Gentile, V. Mastropietro
   Electrons in a lattice with an incommensurate potential
   Journal of Statistical Physics 89 (1997), no. 3-4, 655-708. [MR1658711 (99g:82025)].

10. G. Gentile
    Large deviation rule for Anosov flow
    Forum Mathematicum 10 (1998), no. 1, 89-118. [MR1490140 (98i:58180)].

11. F. Bonetto, G. Gallavotti, G. Gentile, V. Mastropietro
    Quasi linear flows on tori: regularity of their linearization
    Communications in Mathematical Physics 192 (1998), no. 3, 707-736. [MR1620547 (99e:58148)].

12. F. Bonetto, G. Gallavotti, G. Gentile, V. Mastropietro
    Lindstedt series, ultraviolet divergences and Moser's theorem
    Annali della Scuola Normale Superiore di Pisa Classe Scienze (Serie 4) 26 (1998), no. 3, 545-593. [MR1635706 (99i:58132)].

13. G. Benfatto, G. Gentile, V. Mastropietro
    Peierls instability for the Holstein model with rational density
    Journal of Statistical Physics 92 (1998), no. 5-6, 1071-1113. [MR1657864 (99h:82074)].

14. A. Berretti, G. Gentile
    Scaling properties for the radius of convergence of a Lindstedt series: the standard map
    Journal de Mathématiques Pures et Appliquées (9) 78 (1999), no. 2, 159-176. [MR1677673 (2000c:37054)].

15. G. Gallavotti, G. Gentile, V. Mastropietro
    Separatrix splitting for systems with three time scales
    Communications in Mathematical Physics 202 (1999), no. 1, 197-236. [MR1686531 (2000c:37086)].

16. G. Gallavotti, G. Gentile, V. Mastropietro
    Melnikov's approximation dominance. Some examples
    Reviews in Mathematical Physics 11 (1999), no. 4, 451-461. [MR1682687 (2001a:37087)].

17. F. Bonetto, G. Gentile
    On a conjecture for the critical behaviour of KAM tori
    Mathematical Physics Electronic Journal 5 (1999), Paper 4, 8 pp. (electronic). [MR1713650 (2000g:37083)].

18. G. Gallavotti, G. Gentile, V. Mastropietro
    A field theory approach to Lindstedt series for hyperbolic tori in three time scales problems
    Journal of Mathematical Physics 40 (1999), no. 12, 6430-6472. [MR1725867 (2001e:37077].

19. G. Gallavotti, G. Gentile, V. Mastropietro
    On homoclinic splitting problems
    Physica D 137 (2000), no. 1-2, 202-204. [MR1738773 (2000m:37122)].

20. G. Gallavotti, G. Gentile, V. Mastropietro
    Hamilton-Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scale systems
    Nonlinearity 13 (2000), no. 2, 323-340. [MR1745371 (2000m:37121)].

21. F. Bonetto, G. Gentile, V. Mastropietro
    Electric fields on a surface of constant negative curvature
    Ergodic Theory and Dynamical Systems 20 (2000), no. 3, 681-696. [MR1764922 (2001b:37036)].

22. A. Berretti, G. Gentile
    Scaling properties for the radius of convergence of a Lindstedt series: generalized standard maps
    Journal de Mathématiques Pures et Appliquées (9) 79 (2000), no. 7, 691-713. [MR1776500 (2001g:37087)].

23. G. Gentile, V. Mastropietro
    Anderson localization for the Holstein model
    Communications in Mathematical Physics 215 (2000), no. 1, 69-103. [MR1800918 (2002m:82011)].

24. A. Berretti, C. Falcolini, G. Gentile
    The shape of analyticity domains of Lindstedt series: the standard map
    Physical Review E 64 (2001), 015202(R). [MR1860713 (2002h:37118)].

25. A. Berretti, G. Gentile
    Bryuno function and the standard map
    Communications in Mathematical Physics 220 (2001), no. 3, 623-656. [MR1843777 (2002j:37053)]

26. A. Berretti, G. Gentile
    Non-universal behaviour of scaling properties for generalized semistandard and standard maps
    Nonlinearity 14 (2001), no. 5, 1029-1039. [MR1862810 (2002h:37100)].

27. G. Gentile, V. Mastropietro
    Renormalization Group for one-dimensional fermions. A review on mathematical results
    Physics Reports 352 (2001), no. 4-6, 273-437. [MR1862624 (2002h:81152)].

28. M. Bartuccelli, G. Gentile, K.V. Georgiou
    On the dynamics of a vertically driven damped planar pendulum
    The Royal Society of London. Proceedings. Series A. Mathematical, Physical and Engineering Sciences 457 (2001), no. 2016, 3007-3022. [MR1875091 (2002j:70030)].

29. A. Berretti, G. Gentile
    Renormalization Group and field theoretic techniques for the analysis of the Lindstedt series
    Regular and Chaotic Dynamics 6 (2001), no. 4, 389-420. [MR1876532 (2003c:37084)].

30. M. Bartuccelli, G. Gentile, K.V. Georgiou
    On the stability of the upside-down pendulum
    The Royal Society of London. Proceedings. Series A. Mathematical, Physical and Engineering Sciences 458 (2002), no. 2018, 255-269. [MR1889767 (2002m:70032)].

31. M. Bartuccelli, G. Gentile
    Lindstedt series for perturbations of isochronous systems. A review of the general theory
    Reviews in Mathematical Physics 14 (2002), no. 2, 121-171. [MR1883555 (2003a:37081)].

32. G. Gallavotti, G. Gentile
    Hyperbolic low-dimensional invariant tori and summations of divergent series
    Communications in Mathematical Physics 227 (2002), no. 3, 421-460. [MR1910826 (2004f:37082)].

33. A. Berretti, G. Gentile
    Periodic and quasi-periodic orbits for the standard map
    Communications in Mathematical Physics 231 (2002), no. 1, 135-156. [MR1947694 (2003k:37091)].

34. M. Bartuccelli, G. Gentile, K.V. Georgiou
    KAM theory, Lindstedt series and the stability of the upside-down pendulum
    Discrete and Continuous Dynamical Systems Series A 9 (2003), no. 2, 413-426. [MR1952383 (2003k:37090)].

35. M. Bartuccelli, G. Gentile
    On a class of integrable time-dependent dynamical systems
    Physics Letters A 307 (2003), no. 5-6, 274-280. [MR1975826 (2004b:34085)].

36. G. Gentile
    Quasi-periodic solutions for two-level systems
    Communications in Mathematical Physics 242 (2003), no. 1-2, 221-250. [MR2018273 (2005a:81272)].

37. A. Berretti, G. Gentile
    Scaling of the critical function for the standard map: some numerical results
    Nonlinearity 17 (2004), no. 2, 649-670. [MR2039064 (2005i:37046)].

38. M. Bartuccelli, J. Deane, G. Gentile, S. Gourley
    Global attraction to the origin in a parametrically-driven nonlinear oscillator
    Applied Mathematics and Computation 153 (2004), no. 1, 1-11. [MR2063138 (2005d:34077)]

39. G. Gentile
    Pure point spectrum for two-level systems in a strong quasi-periodic field
    Journal of Statistical Physics 115 (2004), no. 5-6, 1605-2620. [MR2066293 (2005m:81352)].

40. G. Gentile, V. Mastropietro
    Convergence of Lindstedt series for the nonlinear wave equation
    Communications on Pure and Applied Mathematics 3 (2004), no. 3, 509-514. [MR2098299 (2005g:35216)].

41. G. Gentile, V. Mastropietro
    Construction of periodic solutions of the nonlinear wave equation with Dirichlet boundary conditions by the Lindstedt series method
    Journal de Mathématiques Pures et Appliquées (9) 83 (2004), no. 8, 1019-1065. [MR2082491].

42. G. Gentile, V. Mastropietro, M. Procesi
    Periodic solutions for completely resonant nonlinear wave equations with Dirichlet boundary conditions
    Communications in Mathematical Physics 256 (2005), no. 2, 437-490. [MR2160800 (2006m:35250)].

43. G. Gentile, G. Gallavotti
    Degenerate elliptic resonances
    Communications in Mathematical Physics 257 (2005), no. 2, 319-362. [MR2164602 (2006e:37111)].

44. G. Gentile, M.V. Bartuccelli, J.H.B. Deane
    Summation of divergent series and Borel summability for strongly dissipative equations with periodic or quasi-periodic forcing terms
    Journal of Mathematical Physics 46 (2005), no. 6, 062704, 21 pp. [MR2149832 (2006d:34118)].

45. G. Gentile, D.A. Cortez, J.C.A. Barata
    Stability for quasi-periodically perturbed Hill's equations
    Communications in Mathematical Physics 260 (2005), no. 2, 403-443. [MR2177325].

46. G. Gentile, T.S. van Erp
    Breakdown of Lindstedt expansion for chaotic maps
    Journal of Mathematical Physics 46 (2005), no. 10, 102702, 20 pp. [MR2178594 (2006e:37051)].

47. M.V. Bartuccelli, J.H.B. Deane, G. Gentile, L. Marsh
    Invariant sets for the varactor equation
    Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 462 (2006), no. 2066, 439-457.

48. G. Gallavotti, G. Gentile, A. Giuliani
    Fractional Lindstedt series
    Journal of Mathematical Physics 47 (2006), no. 1, 012702, 33 pp. [MR2201793 (2006j:37069)].

49. G. Gentile, M. Procesi
    Conservation of resonant periodic solutions for the one-dimensional nonlinear Schrödinger equation
    Communications in Mathematical Physics 262 (2006), no. 3, 533-553. [MR2202301 (2006k:35273)].

50. G. Gentile, M.V. Bartuccelli, J.H.B. Deane
    Quasi-periodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
    Journal of Mathematical Physics 47 (2006), no. 7, 072702, 10 pp. [MR2250293 (2007j:34091)].

51. G. Gentile
    Resummation of perturbation series and reducibility for Bryuno skew-product flows
    Journal of Statistical Physics. 125 (2006), no. 2, 321-361. [MR2270014 (2007m:34102)].

52. O. Costin, G. Gallavotti, G. Gentile, A. Giuliani
    Borel summability and Lindstedt series
    Communications in Mathematical Physics, 269 (2007), no. 1, 175-193. [MR2274467 (2007m:37132)].

53. M.V. Bartuccelli, J.H.B. Deane, G. Gentile
    Globally and locally attractive solutions for quasi-periodically forced systems
    Journal of Mathematical Analysis and Applications 328 (2007), no. 1, 699-714. [MR2285578 (2007k:34171)]

54. G. Gentile
    Degenerate lower-dimensional tori under the Bryuno condition
    Ergodic Theory and Dynamical Systems 27 (2007), no. 2, 427-457. [MR2308140].

55. G. Gentile, M.V. Bartuccelli, J.H.B. Deane
    Bifurcation curves of subharmonic solutions and Melnikov theory under degeneracies
    Reviews in Mathematical Physics 19 (2007), no. 3, 307-348. [MR2316536 (2008c:34084)].

56. M.V. Bartuccelli, J.H.B. Deane, G. Gentile
    Bifurcation phenomena and attractive periodic solutions in the saturating inductor circuit
    Proceedings of The Royal Society of London 463 (2007), no. 2085, 2351-2369. [MR2345231].

57. M.V. Bartuccelli, J.H.B. Deane, G. Gentile
    Periodic attractors for the varactor equation
    Dynamical Systems 22 (2007), no. 3, 365-377. [MR2354971 (2008g:34076)].

58. F. Bonetto, G. Gallavotti, G. Gentile
    A fluctuation theorem in a random environment
    Ergodic Theory and Dynamical Systems 28 (2008), no. 1, 21-47. [MR2380301 (2009k:82054)].

59. M. Bartuccelli, A. Berretti, J. Deane, G. Gentile, S. Gourley
    Selection rules for periodic orbits and scaling laws for a forced damped quartic oscillator
    Nonlinear Analysis. Real World Applications 9 (2008), no. 5, 1966-1988. [MR2441763 (2009g:34144)].

60. G. Gentile, M. Procesi
    Periodic solutions for the Schrödinger equation with nonlocal smoothing nonlinearities in higher dimension
    Journal of Differential Equations 245 (2008), no. 11, 3095-3544. [MR2460026 (2009g:35304)].

61. L. Corsi, G. Gentile
    Melnikov theory to all orders and Puiseux series for subharmonic solutions
    Journal of Mathematical Physics 49 (2008), no. 11, 112701, 29 pp. [MR2468529 (2009m:37141)].

62. M.V. Bartuccelli, J.H.B. Deane, G. Gentile
    Frequency locking in an injection-locked frequency divider equation
    Proceedings of The Royal Society of London Series A. Mathematical, Physical and Engineering Sciences 465 (2009), no. 2101, 283--306. [MR2461376].

63. G. Gentile, M. Procesi
    Periodic solutions for a class of nonlinear partial differential equations in higher dimension
    Communications in Mathematical Physics 289 (2009), no. 3, 863-906. [MR2511654].

64. G. Gentile
    Quasi-periodic motions in strongly dissipative forced systems
    accettato per la pubblicazione da Ergodic Theory and Dynamical Systems.

65. G. Gentile
    Quasi-periodic motions in dynamical systems. Review of a renormalisation group approach
    accettato per la pubblicazione da Journal of Mathematical Physics.

66. M.V. Bartuccelli, J.H.B. Deane, G. Gentile, F. Schilder
    Arnold tongues for a resonant injection-locked frequency divider: analytical and numerical results
    accettato per la pubblicazione da Nonlinear Analysis. Real World Applications.

    2. Proceedings

67. G. Gentile, V. Mastropietro
    A possible mechanism for the KAM tori breakdown
    Hamiltonian systems with three or more degrees of freedom, Proceedings of NATO Adv. Sci. Ins. Ser. C Math. Phys. Sci.
    (S'Agaró, Spagna, 19-30 Giugno 1995), 388-392,
    Ed. C. Simó, Kluwer, Dordrecht, Holland, 1999. [MR1720915].

68. G. Gentile
    Diagrammatic techniques in perturbation theory, and applications
    Symmetry and Perturbation Theory
    (Rome, 16-22 Dicembre 1998), 59-78,
    Eds. A. Degasperis and G. Gaeta, World Scientific, Singapore, 1999. [MR1844106 (2002h:37122)].

69. G. Gentile
    Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori
    SPT 2002: Symmetry and Perturbation Theory
    (Cala Gonone, 19-26 Maggio 2002), 82-89,
    Eds. S. Abenda, G. Gaeta, and S. Walcher, World Scientific, Singapore, 2003. [MR1976659 (2004c:37143)].

70. G. Gentile
    Un nuovo approccio ai sistemi dinamici
    Stato della ricerca e sviluppi futuri. I primi dieci anni di attività della Facoltà di Scienze M.F.N. di Roma Tre
    (Roma, 20-22 Novembre 2002), 289-298,
    Aracne Editrice, Roma, 2003.

71. G. Gentile
    Periodic solutions for zero-mass nonlinear wave equations
    SPT 2004: Symmetry and Perturbation Theory
    (Cala Gonone, 19-26 Maggio 2004), 115-123,
    Eds. G. Gaeta, B. Prinari, S. Rauch-Wojciechowski, and S. Terracini, World Scientific, Hackensack, NJ, 2005. [MR2331213 (2008d:35135)].

72. G. Gentile
    Bryuno numbers and dynamical systems
    Frontiers in Number Theory, Physics, and Geometry, Vol. I: On random matrices, zeta functions, and dynamical systems
    (Les Houches, 9-21 Marzo 2003), 585-599,
    Eds. P.E. Cartier, B. Julia, P. Moussa, and P. Vanhove, Springer, Berlin, 2006. [MR2261105 (2008g:37001)].

    3. Books

73. G. Gallavotti, F. Bonetto, G. Gentile
    Aspects of the ergodic, qualitative and statistical theory of motion
    Springer, Berlin, 2004. [MR2057077 (2005h:37001)].

    4. Encyclopedia articles

74. G. Gentile
    Diagrammatic techniques in perturbation theory
    Encyclopedia of Mathematical Physics, Vol. 2, 54-60
    Eds. J.-P. Françoise, G.L. Naber and T. Sh. Tsun, Elsevier, Oxford, 2006.

75. G. Gentile
    Stability theory and KAM
    Encyclopedia of Mathematical Physics, Vol. 5, 26-32
    Eds. J.-P. Françoise, G.L. Naber and T. Sh. Tsun, Elsevier, Oxford, 2006.

76. G. Gentile
    Diagrammatic methods in classical perturbation theory
    Encyclopedia of Complexity and System Science, Voce 00150
    Ed. R.A. Meyers, Springer, Berlin.

    5. Preprints

77. G. Gentile
    Construction of quasi-periodic response solutions in forced strongly dissipative systems
    Preprint, Roma (2009).