Abstract
We introduce high-dimensional Morse-Smale systems with king-saddles. Every saddle of such system has a separatrix with heteroclinic intersections. We get the necessary and sufficient conditions of conjugacy of Morse-Smale diffeomorphisms with king-saddles. For every polar Morse-Smale system with two saddles on the n-sphere Sn, one proves the existence of a king-saddle. This allows to get the necessary and sufficient conditions of conjugacy for such Morse-Smale diffeomorphisms on Sn, n≥4. We give a simple sufficient condition of the existence of heteroclinic intersections for Morse-Smale systems on S3.
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