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    STUDIA MATHEMATICA - Issue no. 3 / 2008  
         
  Article:   BOOK REVIEWS: MASSIMILIANO BERTI, NONLINEAR OSCILLATIONS OF HAMILTONIAN PDES, PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, VOL. 74, SERIES EDITOR: HAIM BREZIS, BIRKHÄUSER VERLAG, BASEL-BOSTON-BERLIN, 2007, X+235 PP; ISBN- 1.

Authors:  RADU PRECUP. 		 
       
         
  Abstract:  In the study of complex dynamical systems, the simplest invariant manifolds are the equilibria and, next, the periodic orbits. The relevance of periodic solutions for understanding the dynamics of a finite-dimensional Hamiltonian system was highlighted at the end of the 19th century by H. Poincaré in his famous treatise on Celestial Mechanics. In spite of the fact that the set of periodic orbits has measure zero, their study is important due to the possibility, conjectured by Poincaré, of approximating arbitrarily well in long time any solution of a Hamiltonian equation by periodic solutions (with very long periods).  
         
     
         
         
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