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Averaging our nonlinear PDP over individual histories one gets a
linear Liouville equation for the density matrix of the total
system. Tracing over the classical system is, in our case, easily
performed and we then get:

(23) 
where stands for anticommutator, and is a
coupling constant. For written as
,
after some calculations we get a
very simple time evolution:

(24) 
The quantum characteristic exponent, as defined in Ref
[24], is thus
 not a very
useful quantity in our case. The Hausdorff dimension of the limit
set, for the tetrahedral case, has been numerically estimated in
Ref. [25] and shown to decrease from 1.44 to 0.49 while
increases from 0.75 to 0.95. We hope that by publishing
the generating algorithm we will create interest in confirming
these as well as obtaining new results in this field.
Next: 9. How to measure
Up: 4. Notes
Previous: 7. Nonunitarity
20020411