I dont understand how to do this. A diffeomorphism f : [0, 1] → [0, 1] is called Morse-Smale if f has only hyperbolicperiodic points.1. Prove that a Morse-Smale diffeomorphism has only finitely many periodicpoints.2. Prove that a Morse-Smale diffeomorphism of [0, 1] is structurally stable.3. Prove that the map f(x) = x³ + ³r is a Morse-Smale diffeomorphism onthe interval [-1/2,1/2].

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Answered: A diffeomorphism ƒ : [0, 1] → [0, 1] is…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 6E

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