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Full-Text Articles in Physical Sciences and Mathematics
The Entrance Times Of Feigenbaum's Map, Akhtam Dzhalilov, Khamza Kudratov
The Entrance Times Of Feigenbaum's Map, Akhtam Dzhalilov, Khamza Kudratov
Acta of Turin Polytechnic University in Tashkent
It is well known that the Feigenbaum's map ϕ plays main role in theory of universality. The map ϕ is unimodal, even, analitic map of the interval [-1; 1] with one critical point. It is important that the Feigenbaum's map ϕ have infinitely many unstable periodic points and an attractor K of "Cantor type". In present work we investigate the behaviour of entrance times to the set F:
Uniform Distribution For Piecewise-Linear Herman's Maps With Two Breaks, Akhtam Dzhalilov, Khamza Tashkulov
Uniform Distribution For Piecewise-Linear Herman's Maps With Two Breaks, Akhtam Dzhalilov, Khamza Tashkulov
Acta of Turin Polytechnic University in Tashkent
Let h be a piecewise-linear (PL) circle homeomorphism with two break points a0 , c0 and irrational rotation number ρh . Denote by qn , n ≥ 1 the first return times of h and 000(0)():(0)hhaahaσ′−=′+ the jump of h at the point a0 . We prove that for every 1xS∈ the sequence 01log()mod1,1log()nqhDhxnaσ≥ is uniformly distributed on [0,1].
Quasi-Symmetric Distribution Function Of Invariant Measure Of Circle Homeomorphisms With Singularities, U.A. Safarov
Quasi-Symmetric Distribution Function Of Invariant Measure Of Circle Homeomorphisms With Singularities, U.A. Safarov
Acta of Turin Polytechnic University in Tashkent
Let f be a circle homeomorphism with single critical point of non-integer order, that is, 1()()||()dcrcrcrfxxxxxfx−=−−+, 2d>, for some δ-neighborhood ()crUxδ. We prove that, if the homeomorphism f is P-homeomorphism on the set 1\()crSUxδ with irrational rotation numberfρ, then f is topologically conjugate to the pure rotation fρ . Moreover, ϕ is quasi-symmetric if and only if fρ is of bounded type.