Abstract
We consider a compact smooth manifold M. Diff1 (M) denotes the space of C1-diffeomorphisms of M onto itself with the usual C1-topology. In the research of the qualitative theory of dynamical systems there is a desire to find a concept of stability of geometric global structure of orbits such that this stable systems are dense in the space of dynamical systems on M. Structural stability does not satisfy the density condition in Diff1 (M). Tolerance stability (see Section 2 for definition) is a candidate for the density property [7, p. 294]. Concerning tolerance stability there are researches as [6], [7], [8], and [2].
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