Iterates of maps on an interval

Chaotic Behavior of Interval Maps and Total Variations of iterates

Interval maps reveal precious information about the chaotic behavior of general nonlinear systems. If an interval map f : I → I is chaotic, then its iterates f will display heightened oscillatory behavior or profiles as n → ∞. This manifestation is quite intuitive and is, here in this paper, studied analytically in terms of the total variations of f on subintervals. There are four distinctive c...

Random Iterates of Monotone Maps

study of hash functions based on chaotic maps

توابع درهم نقش بسیار مهم در سیستم های رمزنگاری و پروتکل های امنیتی دارند. در سیستم های رمزنگاری برای دستیابی به احراز درستی و اصالت داده دو روش مورد استفاده قرار می گیرند که عبارتند از توابع رمزنگاری کلیددار و توابع درهم ساز. توابع درهم ساز، توابعی هستند که هر متن با طول دلخواه را به دنباله ای با طول ثابت تبدیل می کنند. از جمله پرکاربردترین و معروف ترین توابع درهم می توان توابع درهم ساز md4, md...

Lattice Isomorphisms and Iterates of Nonexpansive Maps

It is easy to see that the I, norm and the sup norm 11. Ilm (Ilxll, = max{Ix, I: 1 I i 5 n)) on I?’ are polyhedral. If E is a finite dimensional Banach space with a polyhedral norm 11. )I, D is a compact subset of E and f: D + D is a nonexpansive map, Weller [2] has shown that for each x E D, there again exists an integer px such that (1.1) holds. The original arguments did not give upper bound...

Moderate deviations for iterates of expanding maps

We provide a mild mixing condition that carries the C.L.T. for normalized empirical means of centered stationary sequence of bounded random variables to the whole range of moderate deviations. It is also key for the exponential convergence of the laws of empirical means. The motivating example for this work are iterates of expanding maps, equipped with their unique invariant measure.