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Applied Mathematics

Ministry of Higher and Secondary Specialized Education of the Republic of Uzbekistan

Journal

Invariant measure

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

The Entrance Times Of Feigenbaum's Map, Akhtam Dzhalilov, Khamza Kudratov Jan 2018

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:


Quasi-Symmetric Distribution Function Of Invariant Measure Of Circle Homeomorphisms With Singularities, U.A. Safarov Jan 2018

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.