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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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