Svanidze, N. V. Small islands of stability in the phase space of the Carleson map. (English. Russian original) Zbl 1120.37026 J. Math. Sci., New York 128, No. 2, 2825-2830 (2005); translation from Zap. Nauchn. Semin. POMI 300, 250-258 (2003). Summary: We consider the Carleson map on the two-dimensional torus and develop an asymptotic theory of islands of an arbitrary period. MSC: 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010) 37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems Keywords:one-preserving map; chaotic map; asymptotic theory of islands × Cite Format Result Cite Review PDF Full Text: DOI References: [1] V. F. Lazutkin, N. V. Petrova, and N. V. Svanidze, ”Small islands of stability in the chaotic sea,” in: Proceedings of the Second International Conference ”Control of Oscillations and Chaos” (COC 2000), Vol. 1, pp. 52–53. · doi:10.1109/COC.2000.873508 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.