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Full-Text Articles in Physical Sciences and Mathematics
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.