Chernov, V. L. A stable foliation to infinity in the phase space of the Hénon map. (English. Russian original) Zbl 1120.37024 J. Math. Sci., New York 128, No. 2, 2716-2720 (2005); translation from Zap. Nauchn. Semin. POMI 300, 72-79 (2003). Summary: We consider the phase space of the quadratic area-preserving Hénon map on the plane. We construct the stable and unstable foliation to infinity and prove their differentiability in the real case. Main conjectures on the behavior of the foliation are discussed for the complex case. We use the presentation of a dynamical system in the form of a continued fraction. MSC: 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37D10 Invariant manifold theory for dynamical systems 30B70 Continued fractions; complex-analytic aspects Keywords:area-preserving map on the plane; behavior of the foliation; continued fraction × Cite Format Result Cite Review PDF Full Text: DOI References: [1] V. F. Lazutkin and M. A. Pankratov, ”A stable foliation to infinity in the complexified phase space of the standard map,” Universitat de Barcelona, Mathematics Preprint Series, No. 183 (1995). [2] A. Ya. Khintchin, Continued Fractions [in Russian], Nauka, Moscow (1978). 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.