## Note on chaos in ray propagation

**Ctirad Matyska**
### Summary

The aim of this note is to mention some potential tools for studies
of chaotical behaviour of rays. First a local exponential divergence
of rays in a phase-space is demonstrated.
Next the possibilities of a study of ray chaos by means of the Lyapunov
exponents for both continuos time-evolution and iterative maps on
Poincare sections are discussed. In the continuos case the Lyapunov
exponents can be obtained from the analyses of the propagator matrices and in
the latter problems their discrete analogies have to be constructed.
The correlation technique is then
shortly pointed out and the employment of wavelet multiresolution analysis
is proposed in the last part of the note.

### Whole paper

The paper is available in
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In: Seismic Waves in Complex 3-D Structures, Report 8,
pp. 71-82, Dep. Geophys., Charles Univ., Prague, 1999.

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