Dense set of negative Schwarzian maps whose critical points have minimal limit sets | Zendy

Alexander Blokh | Zendy; Michał Misiurewicz | Zendy

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Dense set of negative Schwarzian maps whose critical points have minimal limit sets

Author(s) -

Alexander Blokh,

Michał Misiurewicz

Publication year - 1998

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.1998.4.141

Subject(s) - schwarzian derivative , critical point (mathematics) , limit point , limit (mathematics) , set (abstract data type) , interval (graph theory) , mathematics , point (geometry) , omega , pure mathematics , mathematical analysis , combinatorics , geometry , physics , computer science , quantum mechanics , programming language

. We study C,-structural stability of interval maps with negative Schwarz-ian. It turns out that for a dense set of maps critical points either have trajectories attracted to attracting periodic orbits or are persistently recurrent. It follows that for any structurally stable unimodal map the !-limit set of the critical point is minimal.

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