TITLE:
New mechanisms for lack of equipartition of energy

AUTHORS:
Alex Haro
Dept. Mat. Aplicada i Analisi
Univ.  Barcelona
585 Gran Via 
08007, Barcelona, SPAIN

Rafael de la Llave
Department of Mathematics 
University of Texas at Austin 
Austin, TX 78712, USA

ABSTRACT:
We describe several mechanisms that prevent equipartition of energy in 
mechanical systems. In certain regimes, we present a quantitative prediction 
of the relative abundance of orbits exhibiting these mechanisms.
This quantitative prediction is confirmed in numerical experiments.

The main point of this letter is that in many mechanical systems 
the islands -or their higher dimensional analogues 
that we call secondary tori- are much more relevant 
for statistical mechanics than KAM tori. More precisely, we argue that 
the measure of the secondary tori is much larger than that of primary KAM 
tori. Since measure translates into probability in statistical mechanics, 
secondary tori are statistically more relevant than KAM tori.