 9290 Bolte Jens
 Periodic Orbits in Arithmetical Chaos
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Jul 17, 92

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Abstract. Length spectra of periodic orbits are investigated for
some chaotic dynamical systems whose quantum energy spectra
show unexpected statistical properties and for which the
notion of arithmetical chaos has been introduced recently.
These systems are defined as the unconstrained motions
of particles on two dimensional surfaces of constant negative
curvature whose fundamental groups are given by number
theoretical statements (arithmetic Fuchsian groups).
It is shown that the mean multiplicity of lengths l of
periodic orbits grows asymptotically like c*exp(l/2)/l, for
large l. Moreover, the constant c (depending on
the arithmetic group) is determined.
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