Concavity Implies Attraction
نویسنده
چکیده
We consider a skew product with the interval [0,a] as a fiber space and maps in fibers that are concave and fix 0. If the map in the base is an irrational rotation of a circle, then it has been known that under some additional conditions there exists a Strange Nonchaotic Attractor (SNA) for the system. The proofs involved Lyapunov exponents and Birkhoff Ergodic Theorem. We show that the existence of an attractor basically follows solely from the uniform concavity of the maps in the fibers. In particular, it does not depend on the map in the base, so it occurs also in a nonautonomous case. Moreover, we discuss the possible generalizations of the notion of a SNA and show the problems that can occur in the case when the map in the base is noninvertible.
منابع مشابه
Brändén’s Conjectures on the Boros-Moll Polynomials
We prove two conjectures of Brändén on the real-rootedness of the polynomials Qn(x) and Rn(x) which are related to the Boros-Moll polynomials Pn(x). In fact, we show that both Qn(x) and Rn(x) form Sturm sequences. The first conjecture implies the 2-log-concavity of Pn(x), and the second conjecture implies the 3-log-concavity of Pn(x). AMS Classification 2010: Primary 26C10; Secondary 05A20, 30C15.
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