Lochak, P.; Neĭshtadt, A. I. Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian. (English) Zbl 1055.37573 Chaos 2, No. 4, 495-499 (1992). Summary: A Hamiltonian system differing from an integrable system by a small perturbation \(\sim\varepsilon\) is analyzed. According to the Nekhoroshev theorem, the changes in the perturbed motion of the “action” variables of the unperturbed system are small over a time interval which increases exponentially in length \(\varepsilon\) as decreases linearly. If the unperturbed Hamiltonian is a quasiconvex function of these “actions,” the changes in them remain small \((\sim\varepsilon^{1/2n})\) over a time interval on the order of exp(const/\(\varepsilon^{1/2n})\), where \(n\) is the number of degrees of freedom of the system. Cited in 2 ReviewsCited in 31 Documents MSC: 37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems 70H08 Nearly integrable Hamiltonian systems, KAM theory 37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion PDFBibTeX XMLCite \textit{P. Lochak} and \textit{A. I. Neĭshtadt}, Chaos 2, No. 4, 495--499 (1992; Zbl 1055.37573) Full Text: DOI References: [1] Nekhoroshev N. N., Usp. Mat. Nauk 32 pp 5– (1977) · Zbl 0389.70028 · doi:10.1070/RM1977v032n06ABEH003859 [2] Nekhoroshev N. N., Russian Mat. Surveys 32 pp 1– (1977) · Zbl 0389.70028 · doi:10.1070/RM1977v032n06ABEH003859 [3] Nekhoroshev N. N., Tr. Semin. im. I. G. Petrovskogo 5 pp 5– (1979) · Zbl 0389.70028 · doi:10.1070/RM1977v032n06ABEH003859 [4] Benettin G., Celestial Mechanics 37 pp 1– (1955) · Zbl 0602.58022 · doi:10.1007/BF01230338 [5] Arnold V. I., Dokl. Akad. Nauk SSSR 156 pp 11– (1964) [6] Arnold V. I., Sov. Math. Dokl. 5 pp 581– (1964) [7] DOI: 10.1016/0370-1573(79)90023-1 · doi:10.1016/0370-1573(79)90023-1 [8] Neishtadt A. I., Prikl. Mat. Mekh. 48 pp 197– (1984) · Zbl 0571.70022 · doi:10.1016/0021-8928(84)90078-9 [9] Neishtadt A. I., J. Appl. Math. Mech. 48 pp 133– (1984) · Zbl 0571.70022 · doi:10.1016/0021-8928(84)90078-9 [10] Arnold V. I., Usp. Mat. Nauk 18 pp 91– (1963) · Zbl 0135.42701 · doi:10.1070/RM1963v018n06ABEH001143 [11] Arnold V. I., Russian Math. Surv. 18 pp 85– (1963) · Zbl 0135.42701 · doi:10.1070/RM1963v018n06ABEH001143 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.