48 research outputs found
An example derived from Lorenz attractor
We consider a DA-type surgery of the famous Lorenz attractor in dimension 4.
This kind of surgeries have been firstly used by Smale [S] and Ma\~n\'e [M1] to
give important examples in the study of partially hyperbolic systems. Our
construction gives the first example of a singular chain recurrence class which
is Lyapunov stable, away from homoclinic tangencies and exhibits robustly
heterodimensional cycles. Moreover, the chain recurrence class has the
following interesting property: there exists robustly a 2-dimensional
sectionally expanding subbundle (containing the flow direction) of the tangent
bundle such that it is properly included in a subbundle of the finest dominated
splitting for the tangent flow.Comment: 26 pages, 3 figure