Luigi Chierchia


Qualifica: Prof. Ordinario
Email: luigi@mat.uniroma3.it
Ufficio: Largo San Leonardo Murialdo,1 - Pal.C - stanza: 210
Telefono: tel: +390657338235
fax: +390657338072
Ricevimento: MERCOLEDÌ ORE 16:00-18:00
Interessi di Ricerca: Analisi non lineare e sistemi dinamici: equazioni differenziali (ordinarie e alle derivate parziali) con struttura hamiltoniana; mappe simplettiche; sistemi dissipativi; analisi qualitativa: stabilità, orbite periodiche e quasi-periodiche, problemi di "piccoli denominatori"; Meccanica celeste; tecniche locali in analisi non lineare (KAM, Nash-Moser; Nekhoroshev,...)

 
Background:



 
Master ("laurea"), University of Roma "La Sapienza" (1981)  
May 1981- May 1982 served as fireman (military service) 
Ph. D., Courant Institute, NYU (1982-1985) 
Post doc: University of Arizona, ETH (Zürich), École Polytechnique (Palaiseau) 
 
Current position: Full Professor in Mathematical Analisys, Math. Dept., University of Roma Tre  (since 2002) 
Main scientific interests: Nonlinear differential equations and dynamical systems with emphasis on stability problems in Hamiltonian systems 
 
Selected scientific achievements:















 
Classical Hamiltonian systems and Celestial Mechanics: 
  • Whitney smooth interpolation theorem for maximal Lagrangian tori in nearly-integrable Hamiltonian systems 
  • Stability estimates in KAM theory (also computer assisted) 
  • Analytic properties of invariant tori at the break-down threshold 
  • Arnold diffusion (general theory for a priori unstable systems; variational estimates on diffusion speeds) 
  • Direct proof of convergence of Lindstedt series and direct proof of Kolmogorov's theorem on persistence of invariant tori (via graph theory) 
  • Extension of Moser's theory to lower dimensional elliptic tori 
    Existence of invariant tori in physical "sub-models" of the Solar system (computer-assisted) 
  • Dissipative KAM theory for the spin-orbit problem 
  • Completion and extension of Arnold's project on the existence of invariant tori for the planetary N-body problem 
    One dimensional Schrödinger operators: 
  • Spectral theory of quasi-periodic perturbations of periodic Schrödinger operators 
  • Aysmptotic estimates on eigenfunctions 
    Infinite dimensional Hamiltonian systems and PDEs: 
  • Almost periodic solutions for infinite dimensional systems of interacting particles 
  • KAM quasi-periodic solutions for nonlinear wave equations with periodic BC 

Other:























 

 



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