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
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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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