A new shorter proof of the existence of index pairs for discrete dynamical systems is given. Moreover, the index pairs defined in that proof are stable with respect to small perturbations of the generating map. The existence of stable index pairs was previously known in the case of diffeomorphisms and flows generated by smooth vector fields but it was an open question in the general discrete case.

MSC Classifications:

54H20, 54C60, 34C35 show english descriptions Topological dynamics [See also 28Dxx, 37Bxx]
Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
unknown classification 34C35 54H20 - Topological dynamics [See also 28Dxx, 37Bxx]
54C60 - Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
34C35 - unknown classification 34C35

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