Access

You are not currently logged in.

Access JSTOR through your library or other institution:

login

Log in through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Chaotic Functions with Zero Topological Entropy

J. Smítal
Transactions of the American Mathematical Society
Vol. 297, No. 1 (Sep., 1986), pp. 269-282
DOI: 10.2307/2000468
Stable URL: http://www.jstor.org/stable/2000468
Page Count: 14
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Add to My Lists
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Chaotic Functions with Zero Topological Entropy
Preview not available

Abstract

Recently Li and Yorke introduced the notion of chaos for mappings from the class C0(I, I), where I is a compact real interval. In the present paper we give a characterization of the class $M \subset C^0(I, I)$ of mappings chaotic in this sense. As is well known, M contains the mappings of positive topological entropy. We show that M contains also certain (but not all) mappings that have both zero topological entropy and infinite attractors. Moreover, we show that the complement of M consists of maps that have only trajectories approximable by cycles. Finally, it turns out that the original Li and Yorke notion of chaos can be replaced by (an equivalent notion of) δ-chaos, distinguishable on a certain level $\delta > 0$.

Page Thumbnails

  • Thumbnail: Page 
269
    269
  • Thumbnail: Page 
270
    270
  • Thumbnail: Page 
271
    271
  • Thumbnail: Page 
272
    272
  • Thumbnail: Page 
273
    273
  • Thumbnail: Page 
274
    274
  • Thumbnail: Page 
275
    275
  • Thumbnail: Page 
276
    276
  • Thumbnail: Page 
277
    277
  • Thumbnail: Page 
278
    278
  • Thumbnail: Page 
279
    279
  • Thumbnail: Page 
280
    280
  • Thumbnail: Page 
281
    281
  • Thumbnail: Page 
282
    282