Abstract:
For abstract special flows a sufficient condition of absence of mixing is obtained. The result obtained applies to certain classes of smooth flows with nonsingular fixed points on compact orientable surfaces.
Citation:
A. V. Kochergin, “Nonsingular saddle points and the absence of mixing”, Mat. Zametki, 19:3 (1976), 453–468; Math. Notes, 19:3 (1976), 277–286
This publication is cited in the following 22 articles:
Dmitry Dolgopyat, Changguang Dong, Adam Kanigowski, Péter Nándori, “Flexibility of statistical properties for smooth systems satisfying the central limit theorem”, Invent. math., 230:1 (2022), 31
Michael A. Zaks, Alexander Nepomnyashchy, “Subdiffusive and superdiffusive transport in plane steady viscous flows”, Proc. Natl. Acad. Sci. U.S.A., 116:37 (2019), 18245
Michael A. Zaks, Alexander Nepomnyashchy, Nonlinear Systems and Complexity, 20, Advances in Dynamics, Patterns, Cognition, 2017, 61
Bassam Fayad, Adam Kanigowski, “Multiple mixing for a class of conservative surface flows”, Invent. math., 203:2 (2016), 555
Kulaga J., “A Note on the Isomorphism of Cartesian Products of Ergodic Flows”, J. Dyn. Control Syst., 18:2 (2012), 247–267
A. V. Kochergin, “Nondegenerate Saddles and Nonmixing Transformations II”, Math. Notes, 81:1 (2007), 126–129
A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252
B. R. Fayad, M. Lemańczy, “On the ergodicity of cylindrical transformations given by the logarithm”, Mosc. Math. J., 6:4 (2006), 657–672
Michael A. Zaks, NATO Science Series, 182, Chaotic Dynamics and Transport in Classical and Quantum Systems, 2005, 401
A. V. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus. II”, Sb. Math., 195:3 (2004), 317–346
A. V. Kochergin, “Generalizations of theorems on mixing flows with
non-degenerate saddle points on a 2-torus”, Sb. Math., 195:9 (2004), 1253–1270
A. V. Kochergin, “Hölder Time Change and Mixing Rate in a Flow on the Two-Dimensional Torus”, Proc. Steklov Inst. Math., 244 (2004), 201–232
A. V. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus”, Sb. Math., 194:8 (2003), 1195–1224
A. V. Kochergin, “A mixing special flow over a circle rotation with almost
Lipschitz function”, Sb. Math., 193:3 (2002), 359–385
Michael A. Zaks, Arthur V. Straube, “Steady Stokes Flow with Long-Range Correlations, Fractal Fourier Spectrum, and Anomalous Transport”, Phys. Rev. Lett., 89:24 (2002)
Boris Hasselblatt, Anatole Katok, Handbook of Dynamical Systems, 1, 2002, 1
Michael A. Zaks, Arkady S. Pikovsky, Jürgen Kurths, “Symbolic dynamics behind the singular continuous power spectra of continuous flows”, Physica D: Nonlinear Phenomena, 117:1-4 (1998), 77
Michael A. Zaks, Arkady S. Pikovsky, Jürgen Kurths, “Steady Viscous Flow with Fractal Power Spectrum”, Phys. Rev. Lett., 77:21 (1996), 4338
Arkady S. Pikovsky, Michael A. Zaks, Ulrike Feudel, Jürgen Kurths, “Singular continuous spectra in dissipative dynamics”, Phys. Rev. E, 52:1 (1995), 285