A point p is recurrent for f if, for any open interval J about p, there ists n > 0 such that f"(p) E J. Clearly, all periodic points are recurrent. a. Give an example of a non-periodic recurrent point for F, when µ > 2+ V5. b. Give an example of a non-wandering point for F, which is not recur- rent.

A point p is recurrent for f if, for any open interval J about p, there ists n > 0 such that f"(p) E J. Clearly, all periodic points are recurrent. a. Give an example of a non-periodic recurrent point for F, when µ > 2+ V5. b. Give an example of a non-wandering point for F, which is not recur- rent.

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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This problem is Exercise 3, Section 1.7 from Robert L. Devaney's An Introduction to Chaotic Dynamical Systems

A point p is recurrent for f if, for any open interval J about p, there
ists n > 0 such that f"(p) E J. Clearly, all periodic points are recurrent.
a. Give an example of a non-periodic recurrent point for F, when µ >
2+ V5.
b. Give an example of a non-wandering point for F, which is not recur-
rent.

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