Given the tent map T(x) = {2x for x<= 1/2 2-2x for x> 1/2 } Prove that the set of all periodic points of T is dense in [0, 1] and determine the number of points with least periods and their distinct orbits

Given the tent map T(x) = {2x for x<= 1/2 2-2x for x> 1/2 } Prove that the set of all periodic points of T is dense in [0, 1] and determine the number of points with least periods and their distinct orbits

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 21E

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Question

Given the tent map

T(x) =
{2x for x<= 1/2
2-2x for x> 1/2
}

Prove that the set of all periodic points of T is dense in [0, 1] and determine the number of points with least periods and their distinct orbits.

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