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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
icon
Related questions
Question
100%

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.
Transcribed Image Text: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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Systems of Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning