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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 CAMTP - Center for Applied Mathematics and Theoretical Physics}\\
        {\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}\\

%\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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