Non-rigidity for circle homeomorphisms with several break points
نویسندگان
چکیده
منابع مشابه
Examples of non-rigidity for circle homeomorphisms with breaks
We give examples of analytic circle maps with singularities of break type with the same rotation number and the same size of the break for which no conjugacy is Lipschitz continuous. In the second part of the paper, we discuss a class of rotation numbers for which a conjugacy is C1-smooth, although the numbers can be strongly non-Diophantine (Liouville). For the rotation numbers in this class, ...
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Homeomorphisms of the circle were first considered by Poincare* who used them to obtain qualitative results for a class of differential equations on the torus. He classified those which have a dense orbit by showing that they are topologically equivalent to a rotation through an angle incommensurable with IT. However, Denjoy showed that there exist homeomorphisms of the circle without periodic ...
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(The analysis leading to these equat ions will be out l ined in Sect ion 2.) Here, a is a n u m b e r and g (x ) a funct ion def ined on some interval ; bo th a and g(x ) are to be de te rmined . W e are going to cons ider only solut ions with (i) a < 1, (ii) g(x ) a strictly decreas ing funct ion of x, a n d (iii) g(0) = 1. The cond i t ion g(0) = 1 is s imply a normal iza t ion ; if ~ (x ) is...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2017
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2017.121