Abstract:
A detailed proof of the absence of mixing is presented for a special flow constructed by an arbitrary rotation of the circle and by a symmetric function with logarithmic singularities (i.e., a function for which the sums of the coefficients of logarithms for “right” and “left” singularities are equal).
Citation:
A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 252–266; Proc. Steklov Inst. Math., 256 (2007), 238–252