• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

On spectral decomposition of Smale-Vietoris axiom a diffeomorphisms

Dynamical Systems. 2017. Vol. 32. No. 2. P. 221-233.
Isaenkova N., Zhuzhoma E. V.

We introduce Smale–Vietoris diffeomorphisms that include the classical DE mappings with Smale solenoids. We describe the correspondence between basic sets of axiom A Smale–Vietoris diffeomorphisms and basic sets of non-singular axiom A-endomorphisms. For Smale–Vietoris diffeomorphisms of 3-manifolds, we prove the uniqueness of non-trivial solenoidal basic set. We construct a bifurcation between different types of solenoidal basic sets which can be considered as a destruction (or birth) of Smale solenoid.