By Haruo Yoshida (auth.), John Seimenis (eds.)

This quantity comprises invited papers and contributions introduced on the overseas convention on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland in the course of the summer season of 1993. The convention was once supported by means of the NATO clinical and Environmental Affairs department as a complicated examine Workshop. in truth, it used to be the 1st clinical convention in all jap Europe supported through NATO. The assembly used to be anticipated to set up contacts among East and West specialists in addition to to review the present state-of-the-art within the region of Hamiltonian Mechanics and its purposes. i'm convinced that the casual surroundings of town of Torun, the birthplace of Nicolaus Copernicus, prompted many necessary medical exchanges. the 1st thought for this cnference used to be performed via Prof Andrzej J. Maciejewski and myself, greater than years in the past, in the course of his stopover at in Greece. It used to be deliberate for approximately 40 famous scientists from East and West. at the moment participation of a scientist from jap Europe in an setting up Committee of a NATO convention used to be now not allowed. yet continually there's the 1st time. Our plans for this kind of "small" convention, as a primary try within the new ecu state of affairs -the Europe borderless -quickly kicked the bucket. The names of our invited audio system, professionals of their box, have been a magnet for plenty of colleagues from all around the world.

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Poles in the angle 8 form two families of real lines parallel to the imaginary axis ( or rays in z = eiB ); in the limit of a real irrational frequency these lines become 35 dense creating a natural boundary in the analyticity strip. This picture is explained analytically at the level of homologic equation when the non linear term has itself a singularity. The Siegel problem exhibits the same features when the frequency is complexified and the same correspondence between the homologic level and the complete solution exists.

3:3, pp. 377-402. 6. A. D. Bruno, 1978, On periodic flybys of the moon, Preprint No. 91 of Inst. , Moscow (in Russian). English version: Celest. Mech, 1981, 24, pp. 255-268. 7. A. D. Bruno, 1992, General approach to a study of compl'icated bifurcations, Prikladnaya Mekhanika, 28:12, pp. 83-86 (in Russian). English translation in Soviet Applied Mathematics. 8. A. D. Bruno, 1993, Multiple periodic solutions of the restricted three-body problem in the Sun-Jupiter case, Preprint of Inst. , Moscow (in Russian), to appear.

Figure 3. Behaviour of the function c(e). The function c(e) is plotted against e. The loglo scale is used for e. 5]. 5] 30 By using (79) and (80) and assuming f38/t:. not too small (to be checked later), the dominant part, Pi> of the coefficient of the harmonic (76) in (67) is given by ~= (t:. )2( Fj-3)! ) ) . (81 ) By taking logarithms and skipping some terms simply linear in j (where the contribution of the other decompositions in (77) is included), we have In p. J ~ 'Y+2 'Y + 1 ['Y (1 - ~) In 2 - In 'Y + 1) + (1 + In 'Y] 'Y j 'Y+2 'Y 'Y + 1 j ( .

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