New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here


by: Reuben Hudson DDS
Reuben Hudson DDS
GPA 3.55


Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Reuben Hudson DDS on Friday October 30, 2015. The Class Notes belongs to MATH 397 at University of Massachusetts taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/232225/math-397-university-of-massachusetts in Mathematics (M) at University of Massachusetts.

Similar to MATH 397 at UMass


Reviews for ST


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/30/15
Math 3970 10101 De nitions about attracting and repelling7corrected Throughout let 1 A 7 A be a function from a subset A of R into itself For each nonnegative integer n denote by f the nth iterate of 1 so that also 1 A 7 A Thus 1 0 is the identity function of A the rst iterate f1 f the second iterate f2 f o 1 etc Then for a point z E A the set f m n O 1 23 is the orbit of z under 1 De nition 1 An z E A is called a xed point of 1 when fz m If x is a xed point of 1 then f m z for every n O 1 2 3 and so the orbit of z under 1 is just the onepoint set De nition 2 Let p be a xed point of 1 Say that p attracts a point z E A and z is attracted to p when 1mm 1 7 p The basin of attraction of p is the set of all points z E A that are attracted to p The xed point p as well as its orbit is said to attract and to be an attractor when its basin of attraction includes A O p 7 619 l 6 for some 6 gt 0 In other words p is an attractor when all points of A that are suf ciently close to p are attracted to p De nition 3 Corrected Let p be a xed point of 1 Then p as well as its orbit is said to repel and to be a repellor when for some 6 gt O for each x E A p7 6p 6 with z 31 p there is at least one power 71 such that f z p 7 619 6 In other words p repels when for some 6 gt O the orbit of each point z E A O p7 6p 6 other than ofp itself does not remain in p 7 619 l 6 De nition 4 A point p E A is said to be a periodic point7and its orbit is said to be a periodic orbit7if there is some integer k 2 2 for which fkp p In this case the least such k is called the prime period of p According to the preceding de nition a xed point is not considered to be periodic Some authors do so consider it In any case you could regard a xed point as a sort of degenerate case of a periodic point Suppose p is a periodic point of f with period k The also fk1p fp fk2p f2p etc Thus the entire orbit of p reduces to just the nite set 19 fp f2p fk 1p consisting of exactly k distinct points If p is a periodic point of f with period k then p is a xed point of the kth iterate fk A 7 A In this case we may consider the new De nition 5 Let p be a periodic point of f with period k Consider instead of f the function fk A e A Say that p attracts or repels when p attracts or repels respectively for fk In this situation also call the periodic orbit ofp under 1 a periodic attractor or periodic repellor respectively


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Janice Dongeun University of Washington

"I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.