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Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 16CM

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A diffeomorphism f : [0, 1] → [0, 1] is called Morse-Smale if f has only hyperbolic
periodic points.
1. Prove that a Morse-Smale diffeomorphism has only finitely many periodic
points.
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 on
the interval [-1/2,1/2].

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