0 a seat for a rider -- sadel; -sadel
The bicycle saddle is too high.
1 (opposite unsaddle) to put a saddle on -- sadle
He saddled his horse and rode away.
Moreover, any chain recurrence class containing saddles having different indices has a robust cycle.
Consider a diffeomorphism f with a co-index 1 cycle associated with a pair of saddles.
By [14], open and densely, these diffeomorphisms have saddles of different consecutive indices.
We prove that these cycles generate (by perturbations) new heterodimensional cycles associated with saddles with non-trivial homoclinic classes.
The theorems in 4 and 5 are stated in terms of heteroclinic points between fixed point saddles.
As a consequence, we can extend the homeomorphism to the stable manifolds of the saddles in the following way.
However, the center conditions apply also to the 1:-1 resonant saddles; in fact, we should take only the equation for center (not inequalities).
Moreover, the indices of some of these saddles may not belong to the interval of indices of the saddles of the class.
