61
Views
1
CrossRef citations to date
0
Altmetric
Articles

Dynamics of three-dimensional A-diffeomorphisms with two-dimensional attractors and repellers

ORCID Icon, ORCID Icon & ORCID Icon
Pages 1275-1286 | Received 04 Mar 2022, Accepted 02 Jun 2022, Published online: 01 Jul 2022

References

  • M. Barinova, On existence of an energy function for ω-stable surface diffeomorphisms, Lobachevskii J. Math. 42 (2021), pp. 3317–3323.
  • D. Baranov, V. Grines, O. Pochinka, and E. Chilina, On classification of periodic maps on the 2-torus. arXiv preprint arXiv:2112.01256. 2021.
  • M. Barinova, V. Grines, O. Pochinka, and B. Yu, Existence of an energy function for three-dimensional chaotic “sink-source” cascades, Chaos: Interdiscip. J. Nonlinear Sci. 31 (2021), Article ID 063112.
  • A.W. Brown, Nonexpanding attractors: Conjugacy to algebraic models and classification in 3-manifolds, J. Mod. Dyn. 4 (07 2010), pp. 517–548.
  • C. Conley, Isolated Invariant Sets and the Morse Index, Vol. 38, American Mathematical Society, CBMS, Providence, RI, 01 1978.
  • V. Grines, On topological conjugacy of diffeomorphisms of a two-dimensional manifold onto one-dimensional orientable basic sets i, Trans. Mosc. Math. Soc. 32 (1975), pp. 31–56.
  • V. Grines and E. Zhuzhoma, On structurally stable diffeomorphisms with codimension one expanding attractors, Trans. Am. Math. Soc. 357(2) (2004), pp. 617–667.
  • V.Z. Grines, V.S. Medvedev, and E.V. Zhuzhoma, New relations for Morse–Smale systems with trivially embedded one-dimensional separatrices, Sb. Math. 194 (2003), pp. 979–1007.
  • V.Z. Grines, V.S. Medvedev, and E.V. Zhuzhoma, On surface attractors and repellers in 3-manifolds, Math. Notes 78(5–6) (2005), pp. 757–767.
  • V. Grines, F. Laudenbach, and O. Pochinka, Dynamically ordered energy function for Morse–Smale diffeomorphisms on 3-manifolds, Proc. Stekl. Inst. Math. 278 (01 2012),pp. 27–40.
  • V. Grines, M. Noskova, and O. Pochinka, Construction of an energy function for a-diffeomorphisms of two-dimensional non-wandering sets on 3-manifolds, Middle Volga Math. Soc. J. 17 (2015), pp. 12–17.
  • V. Grines, M. Noksova, and O. Pochinka, The construction of an energy function for three-dimensional cascades with a two-dimensional expanding attractor, Trans. Mosc. Math. Soc. 76 (2015), pp. 237–249.
  • V. Grines, T. Medvedev, and O. Pochinka, Dynamical Systems on 2- and 3-Manifolds, Vol. 46, Springer, Switzerland, 01 2016.
  • T.V. Medvedev and O.V. Pochinka, The wild Fox–Artin arc in invariant sets of dynamical systems, Dyn. Syst. 33(4) (2018), pp. 660–666.
  • S.E. Nowhouse, Hyperbolic limit sets, Trans. Am. Math. Soc. 167 (1972), pp. 125–150.
  • D. Pixton, Wild unstable manifolds, Topology 16 (12 1977), pp. 167–172.
  • R. Plykin, The topology of basis sets for smale diffeomorphisms, Math. USSR-Sb. 13 (1971), pp. 297–307.
  • R.V. Plykin, On the geometry of hyperbolic attractors of smooth cascades, Russian Math. Surv. 39(6) (1984), pp. 85–131.
  • S. Smale, Differentiable dynamical systems, Bull. Am. Math. Soc. 73 (11 1967), pp. 747–817.
  • E.V. Zhuzhoma and V.S. Medvedev, On non-orientable two-dimensional basic sets on3-manifolds, Sb. Math. 193(6) (2002), pp. 869–888.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.