#9 only The following exercises apply to the tent map2zT2(z) =2(1 - z) 1/2 SIS1= }. To describe theNote that the maximum of T is 1 and occurs at zdynamics of T2 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...s-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.6. Prove that S:I - E, is one-to-one, where S(2) is defined as in §1.7.IS7. Prove that o o S = So Tz.8. Prove that Tz has exactly 2" periodic points of period n.9. Prove that T2 is chaotic on I.

Name: #9 only The following exercises apply to the tent map2zT2(z) =2(1 - z)
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: #9 only The following exercises apply to the tent map2zT2(z) =2(1 - z) 1/2 SIS1= }. To describe theNote that the maximum of T is 1 and occurs at zdynamics of T2 via symbolic dy namics, we thus need to modify E2 somewhatsince there is an ambiguity in