The bifurcation of homoclinic orbits of maps of the interval
Open Access
- 1 June 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 2 (2) , 131-138
- https://doi.org/10.1017/s0143385700001462
Abstract
Relationships involving homoclinic orbits of various periods and the Sarkovskii stratification are given and corresponding bifurcation properties are derived. It is shown that if a continuous map has one homoclinic periodic orbit, it has infinitely many. In any family of C1 maps going from zero to positive entropy, infinitely many homoclinic bifurcations occur, involving periods which are successively smaller powers of two.Keywords
This publication has 5 references indexed in Scilit:
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