#10 only The following exercises apply to the tent map2zT2(z) =2(1-z) 1/2 S=S1. To describe theNote that the maximum of T is 1 and occurs at z =dynamics of T via symbolic dy namics, we thus need to modify E2 somewhatsince there is an ambiguity in the sequence associated to any rational numberof the form p/2 where p is an integer. For example, 1/2 may be described byeither (11000...) or (01000...). To remedy this, we identify any two sequencesof the form (so ...3-1 1000...), where 0 or 1. For example, the sequences(1101000...) and (1111000...) are to be thought of as representing the samepoint. Let E denote E2 with these identifications.Prove that S:I→ E, is one-to-one, where S(z) is defined as in $1.7.7. Prove that o o S = So T2.8. Prove that Tz has exactly 2" periodic points of period n.6.%3D9. Prove that T2 is chaotic on 1.10. Prove that Tz is topologically conjugate to the quadratic map F(z) =4z(1 – z).%3D

Name: #10 only The following exercises apply to the tent map2zT2(z) =2(1-z)
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: #10 only The following exercises apply to the tent map2zT2(z) =2(1-z) 1/2 S=S1. To describe theNote that the maximum of T is 1 and occurs at z =dynamics of T via symbolic dy namics, we thus need to modify E2 somewhatsince there is an ambiguity in the