Abstract
We show for the class [Formula: see text] of all C∞, transitive and topologically conjugate to algebraic polynomials interval self-maps the following stability type property: the class [Formula: see text] has no isolated points and for every [Formula: see text] and any ε arbitrary small positive real number there exists a map [Formula: see text] sharing with f the same fixed points except one and such that ‖ f - g ‖1 = ε. On the contrary, we also show for each [Formula: see text] that the re exists a C∞ interval self-map topologically conjugate to a polynomial, not transitive and ‖ ⋅ ‖1-arbitrary close to the map f.
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