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        Naklju\v cnost klasi\v cnega deterministi\v cnega gibanja\\[0.9cm]
       
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        MARKO ROBNIK\\[0.9cm]                        
        {\em CAMTP - Center za uporabno matematiko in teoreti\v cno fiziko}\\
        {\em Univerza v Mariboru, Krekova 2, SI-2000 Maribor, Slovenia}\\
        {\em Robnik@uni-mb.si  $\bullet$ www.camtp.uni-mb.si}\\[0.7cm]
       
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Predstavil bom nekaj novih univerzalnih vidikov difuzije v klasi\v cnih
deterministi\v cnih in kaoti\v cnih dinami\v cnih sistemih, \v se posebej
v Hamiltonovih sistemih, med katerimi je Henon-Heiles sistem
pomemben paradigmati\v cni primer, kot sistem dveh nelinearno sklopljenih 
harmonskih oscilatorjev. Z nara\v s\v canjem jakosti sklopitve se pove\v cuje
velikost kaoti\v cne komponente, kakor tudi naklju\v cnost klasi\v cnega
kaoti\v cnega gibanja znotraj te komponente. Pri razvoju teorije bomo
najprej obravnavali ergodi\v cne (povsem kaoti\v cne sisteme), potem pa
sisteme me\v sanega tipa, kot je n.pr. Henon-Heiles sistem, s tipi\v cnim
KAM scenarijem. Obravnavali bomo tudi nekaj posplo\v sitev z upo\v stevanjem
korelacij. Nazadnje bom pojasnil pomen teh raziskav v kontekstu
stacionarnega kvantnega kaosa, namre\v c za strukturo stacionarnih
lastnih funkcij in za statisti\v cne lastnosti energijskih spektrov.

{\bf Reference}\\

\newcommand\itm[2]{\parbox[t]{1cm}{#1}\parbox[t]{14cm}{#2}\\[1mm] }

\itm{[1]} {M. Robnik, J. Dobnikar, A. Rapisarda, T. Prosen and M. Petkov\v sek,
{\em Journal of Physics A: Mathematical \& General} {\bf 30} (1997) L803-L813.}
\itm{[2]} {T. Prosen and M. Robnik, {\em Journal of Physics A: Mathematical \& General} {\bf 31} (1998) L345-L353.}
\itm{[3]} {M. Robnik, T. Prosen and J. Dobnikar,
{\em Journal of Physics A: Mathematical \& General} {\bf 32} (1999) 1147-1162.}  
\itm{[4]} {M. Robnik, {\em Nonlinear Phenomena in Complex Systems} (Minsk) 
{\bf 1} No. 1 (1998) 1-22.}
\itm{[5]} {T. Prosen and M. Robnik,
{\em Journal of Physics A: Mathematical \& General} {\bf 32} (1999) 1863-1873.}
\itm{[6]} {J. Malovrh and T. Prosen, 
{\em Journal of Physics A: Mathematical \& General} {\bf 35} 
(2002) 2483-2490.} 


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        Randomness  in classical deterministic motion\\[0.9cm]
       
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        MARKO ROBNIK\\[0.9cm]                        
        {\em CAMTP - Center for Applied Mathematics and Theoretical Physics}\\
        {\em University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia}\\
        {\em Robnik@uni-mb.si  $\bullet$ www.camtp.uni-mb.si}\\[0.7cm]
       
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I shall discuss some new universal aspects of diffusion
in classical deterministic and chaotic dynamical systems, 
especially in Hamiltonian systems, one of the important paradigmatic
examples being the Henon-Heiles system, which is an example
of two nonlinearly coupled harmonic oscillators. As the strength of
the coupling increases, the size of the chaotic component
increases, and so does the randomness of classical chaotic motion
inside. In setting up a theory first ergodic (fully
chaotic) systems will be discussed, and then the mixed type
systems, like Henon-Heiles system, with a typical KAM scenario. 
Some generalizations by treating the correlations will be presented. 
Finally, I shall explain the relevance of these studies in 
the context of problems in stationary quantum chaos, namely 
the structure of stationary eigenfunctions and the statistical 
properties of the energy spectra.



{\bf References}\\


\itm{[1]} {M. Robnik, J. Dobnikar, A. Rapisarda, T. Prosen and M. Petkov\v sek,
{\em Journal of Physics A: Mathematical \& General} {\bf 30} (1997) L803-L813.}
\itm{[2]} {T. Prosen and M. Robnik, {\em Journal of Physics A: Mathematical \& General} {\bf 31} (1998) L345-L353.}
\itm{[3]} {M. Robnik, T. Prosen and J. Dobnikar,
{\em Journal of Physics A: Mathematical \& General} {\bf 32} (1999) 1147-1162.}  
\itm{[4]} {M. Robnik, {\em Nonlinear Phenomena in Complex Systems} (Minsk) 
{\bf 1} No. 1 (1998) 1-22.}
\itm{[5]} {T. Prosen and M. Robnik,
{\em Journal of Physics A: Mathematical \& General} {\bf 32} (1999) 1863-1873.}
\itm{[6]} {J. Malovrh and T. Prosen, 
{\em Journal of Physics A: Mathematical \& General} {\bf 35} 
(2002) 2483-2490.} 



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