کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900331 | 1631560 | 2018 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A remark on Denjoy's inequality for PL circle homeomorphisms with two break points
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
It is well known that for a P-homeomorphism f of the circle S1=R/Z with irrational rotation number Ïf the Denjoy's inequality |logâ¡Dfqn|â¤V holds, where V is the total variation of logâ¡Df and qn, nâ¥1, are the first return times of f. Let h be a piecewise-linear (PL) circle homeomorphism with two break points a0, c0, irrational rotation number Ïh and total jump ratio Ïh=1. Denote by Bn(h) the partition determined by the break points of hqn and by μh the unique h-invariant probability measure. It is shown that the derivative Dhqn is constant on every element of Bn(h) and takes either two or three values. Furthermore we prove, that logâ¡Dhqn can be expressed in terms of μh-measures of some intervals of the partition Bn(h) multiplied by the logarithm of the jump ratio Ïh(a0) of h at the break point a0.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 458, Issue 1, 1 February 2018, Pages 508-520
Journal: Journal of Mathematical Analysis and Applications - Volume 458, Issue 1, 1 February 2018, Pages 508-520
نویسندگان
Akhtam Dzhalilov, Alisher Jalilov, Dieter Mayer,