1,028 research outputs found
Liapunov Multipliers and Decay of Correlations in Dynamical Systems
The essential decorrelation rate of a hyperbolic dynamical system is the
decay rate of time-correlations one expects to see stably for typical
observables once resonances are projected out. We define and illustrate these
notions and study the conjecture that for observables in , the essential
decorrelation rate is never faster than what is dictated by the {\em smallest}
unstable Liapunov multiplier
Extensive Properties of the Complex Ginzburg-Landau Equation
We study the set of solutions of the complex Ginzburg-Landau equation in
. We consider the global attracting set (i.e., the forward map of
the set of bounded initial data), and restrict it to a cube of side .
We cover this set by a (minimal) number of balls of radius
in \Linfty(Q_L). We show that the Kolmogorov -entropy
per unit length,
exists. In particular, we bound by \OO(\log(1/\epsilon), which
shows that the attracting set is smaller than the set of bounded analytic
functions in a strip. We finally give a positive lower bound:
H_\epsilon>\OO(\log(1/\epsilon))Comment: 24 page
Trees of nuclei and bounds on the number of triangulations of the 3-ball
Based on the work of Durhuus-J{\'o}nsson and Benedetti-Ziegler, we revisit
the question of the number of triangulations of the 3-ball. We introduce a
notion of nucleus (a triangulation of the 3-ball without internal nodes, and
with each internal face having at most 1 external edge). We show that every
triangulation can be built from trees of nuclei. This leads to a new
reformulation of Gromov's question: We show that if the number of rooted nuclei
with tetrahedra has a bound of the form , then the number of rooted
triangulations with tetrahedra is bounded by
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