caa a22 4500 467987009 CHVBK 20180323112534.0 cr unu---uuuuu 170328e19900601xx s 000 0 eng 10.1007/BF00050713 doi (NATIONALLICENCE)springer-10.1007/BF00050713 Šidlichovský M. Astronomical Institute of the Czechoslovak Academy of Sciences, 6, 120 23 Praha 2, Budečská, Czechoslovakia aut The existence of a chaotic region due to the overlap of secular resonances ν5 and ν6 [Elektronische Daten] [M. Šidlichovský] A nonlinear theory of secular resonances is developed. Both terms corresponding to secular resonances ν5 and ν6 are taken into account in the Hamiltonian. The simple overlap criterion is applied and the condition for the overlap of these resonances is found. It is shown that in given approximation the value p = (1 - e2)1/2(1 - cosI) is an integral of motion, where the mean eccentricity e and mean inclination I are obtained by eliminating short-period perturbations as well as the nonresonant terms from the planets. The overlap criterion yields a critical value of parameter p depending on the semi-major axis a of the asteroid. For p greater than the critical value, resonance overlap occurs and chaotic motion has to be expected. A mapping is presented for fast calculation of the trajectories. The results are illustrated by level curves in surfaces of section method. Kluwer Academic Publishers, 1990 Asteroid belt nationallicence secular resonances nationallicence chaotic behavior nationallicence overlap of resonances nationallicence Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/2(1990-06-01), 177-196 0923-2958 49:2<177 1990 49 10569 https://doi.org/10.1007/BF00050713 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00050713 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Šidlichovský M. Astronomical Institute of the Czechoslovak Academy of Sciences, 6, 120 23 Praha 2, Budečská, Czechoslovakia aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/2(1990-06-01), 177-196 0923-2958 49:2<177 1990 49 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer