Abstract:
It is known that a nontrivial attractor coexists with trivial basic sets in the nonwandering set of an $\Omega$-stable 3-diffeomorphism if and only if it is either nonorientable one-dimensional or (orientable or not) expanding and two-dimensional. Examples of such diffeomorphisms were constructed previously, with the exception of the case of a nonorientable two-dimensional attractor. The paper fills this gap. In addition, it is constructively shown that the diffeomorphism obtained has an energy function, which extends thereby the class of cascades with global Lyapunov function whose set of critical points coincides with the nonwandering set of the dynamical system.
Bibliography: 20 titles.
Keywords:basic set, $\Omega$-stability, expanding attractor, generalized Plykin attractor, energy function.
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