Wagener, Florian A note on Gevrey regular KAM theory and the inverse approximation lemma. (English) Zbl 1036.37022 Dyn. Syst. 18, No. 2, 159-163 (2003). Summary: A theorem of the type Kolmogorov-Arnold-Moser holds for small real analytic perturbations of a family of parallel flows on a torus, yielding conjugacies to Diophantine parallel flows that depend Whitney-Gevrey regularly on parameters. This follows from an adaptation of the inverse approximation lemma. The method of proof is general and extends to a wide range of problems of KAM type. Cited in 1 ReviewCited in 17 Documents MSC: 37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion Keywords:perturbations; parallel flows PDFBibTeX XMLCite \textit{F. Wagener}, Dyn. Syst. 18, No. 2, 159--163 (2003; Zbl 1036.37022) Full Text: DOI References: [1] Bonet J., Studia Mathematica 99 pp 155– (1991) [2] DOI: 10.1007/BF02218818 · Zbl 0820.58050 · doi:10.1007/BF02218818 [3] Broer H. W., Quasi-periodic Motions in Familes of Dynamical Systems, Lecture Notes in Mathematics 1645 (1996) [4] Broer H. W., Unfoldings and Bifurcations of Quasi-periodic Tori, Memoirs of the AMS 421 (1990) [5] Huitema G. B., Unfoldings of quasi-periodic tori (1988) · Zbl 0820.58050 [6] DOI: 10.1007/BF01399536 · Zbl 0149.29903 · doi:10.1007/BF01399536 [7] DOI: 10.1007/PL00001004 · Zbl 0970.37050 · doi:10.1007/PL00001004 [8] DOI: 10.1007/PL00001005 · Zbl 1002.37028 · doi:10.1007/PL00001005 [9] DOI: 10.1002/cpa.3160350504 · Zbl 0542.58015 · doi:10.1002/cpa.3160350504 [10] Stein E. M., Singular Integrals and the Differentiability Properties of Functions (1970) · Zbl 0207.13501 [11] DOI: 10.1002/cpa.3160280104 · Zbl 0309.58006 · doi:10.1002/cpa.3160280104 [12] DOI: 10.1002/cpa.3160290104 · Zbl 0334.58009 · doi:10.1002/cpa.3160290104 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.