A triangular map with homoclinic orbits and no infinite ω-limit set containing periodic points |
| |
Authors: | F Balibrea |
| |
Institution: | a Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain b Mathematical Institute, Silesian University, 746 01 Opava, Czech Republic |
| |
Abstract: | Recently, Forti, Paganoni and Smítal constructed an example of a triangular map of the unite square, F(x,y)=(f(x),g(x,y)), possessing periodic orbits of all periods and such that no infinite ω-limit set of F contains a periodic point. In this note we show that the above quoted map F has a homoclinic orbit. As a consequence, we answer in the negative the problem presented by A.N. Sharkovsky in the eighties whether, for a triangular map of the square, existence of a homoclinic orbit implies the existence of an infinite ω-limit set containing a periodic point. It is well known that, for a continuous map of the interval, the answer is positive. |
| |
Keywords: | primary 37B20 37B40 37B55 secondary 26A18 54H20 |
本文献已被 ScienceDirect 等数据库收录! |
|