科研之友
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摘要
It is known that under the certain conditions on the coefficient the Ricker difference equation (or map) has a fixed point that is globally asymptotically stable with respect to the positive reals. We show here that under the same conditions, the Ricker equation with almost periodic coefficient has a globally asymptotically stable almost periodic solution with the same frequency module as the coefficient. This is accomplished by showing that the omega limit set Omega of an asymptotically stable solution is a covering space of the omega limit set of the coefficients and the flow on Omega is uniquely reversible. We provide a unified framework that allows us to conclude that any system of maps in finite dimensions that has an orbit that is bounded and whose omega limit set is asymptotically stable, also has the property that certain attributes of the coefficients (periodicity, almost periodicity) can be carried over, or lifted to the solution. In particular if the successive compositions are bounded and have Frechet derivatives with spectrum inside the unit circle in the complex plane then the above conclusions apply.
- 出版日期2017
