scholarly journals Topological weak mixing and quasi-Bohr systems

2005 ◽  
Vol 148 (1) ◽  
pp. 277-304 ◽  
Author(s):  
E. Glasner
Keyword(s):  
Weak Mixing ◽  
Topological Weak Mixing

scholarly journals On weak mixing, minimality and weak disjointness of all iterates

2011 ◽  
Vol 32 (5) ◽  
pp. 1661-1672 ◽  
Author(s):  
DOMINIK KWIETNIAK ◽  
PIOTR OPROCHA
Keyword(s):  
Topological Dynamical System ◽  
Multiple Recurrence ◽  
Weak Mixing ◽  
Compact Metric Space ◽  
Open Questions ◽  
Weakly Mixing ◽  
Recurrence Theorem ◽  
Topological Weak Mixing ◽  
Mixing Property ◽  
Transitive System

AbstractThis article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map f×f2×⋯×fm, where f:X→X is a topological dynamical system on a compact metric space. The theorem stating that a weakly mixing and strongly transitive system is Δ-transitive is extended to a non-invertible case with a simple proof. Two examples are constructed, answering the questions posed by Moothathu [Diagonal points having dense orbit. Colloq. Math. 120(1) (2010), 127–138]. The first one is a multi-transitive non-weakly mixing system, and the second one is a weakly mixing non-multi-transitive system. The examples are special spacing shifts. The latter shows that the assumption of minimality in the multiple recurrence theorem cannot be replaced by weak mixing.

On local aspects of topological weak mixing in dimension one and beyond

2011 ◽  
Vol 202 (3) ◽  
pp. 261-288 ◽  
Author(s):  
Piotr Oprocha ◽  
Guohua Zhang
Keyword(s):  
Weak Mixing ◽  
Dimension One ◽  
Topological Weak Mixing

Topological weak-mixing of interval exchange maps

1997 ◽  
Vol 17 (5) ◽  
pp. 1183-1209 ◽  
Author(s):  
A. NOGUEIRA ◽  
D. RUDOLPH
Keyword(s):  
Measure Zero ◽  
Interval Exchange ◽  
Weak Mixing ◽  
Interval Map ◽  
Constant Height ◽  
Interval Lengths ◽  
Topological Weak Mixing ◽  
Interval Exchange Maps

An interval map with only one discontinuity is isomorphic to a rotation of the circle, and has continuous eigenfunctions. What we show here is that for almost every choice of lengths of the intervals, this is the only way an irreducible interval exchange can have a somewhere continuous eigenfunction. We show slightly more, considering certain towers over the interval exchange, showing that outside of a set of choices for interval lengths of measure zero these have a somewhere continuous eigenfunction only if they are isomorphic to either a rotation, or a tower of constant height over an interval exchange.

scholarly journals Topological weak mixing and diffusion at all times for a class of Hamiltonian systems

2021 ◽  
pp. 1-15
Author(s):  
BASSAM FAYAD ◽  
MARIA SAPRYKINA
Keyword(s):  
Hamiltonian Systems ◽  
Weak Mixing ◽  
Topological Weak Mixing ◽  
And Diffusion ◽  
Strong Diffusion ◽  
Diffusion Properties

Abstract We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples are obtained by AbC constructions with several frequencies.

On local aspects of topological weak mixing, sequence entropy and chaos

2013 ◽  
Vol 34 (5) ◽  
pp. 1615-1639 ◽  
Author(s):  
PIOTR OPROCHA ◽  
GUOHUA ZHANG
Keyword(s):  
Dynamical Systems ◽  
Qualitative Theory ◽  
Broad Sense ◽  
Weak Mixing ◽  
Sequence Entropy ◽  
Weakly Mixing ◽  
Topological Weak Mixing ◽  
Topological Sequence Entropy ◽  
Mixing Sequence

AbstractIn this paper we show that for every$n\geq 2$there are minimal systems with perfect weakly mixing sets of order$n$and all weakly mixing sets of order$n+ 1$trivial. We present some relations between weakly mixing sets and topological sequence entropy; in particular, we prove that invertible minimal systems with non-trivial weakly mixing sets of order three always have positive topological sequence entropy. We also study relations between weak mixing of sets and other well-established notions from qualitative theory of dynamical systems like (regional) proximality, chaos and equicontinuity in a broad sense.

New proofs that weak mixing is generic

1976 ◽  
Vol 32 (3) ◽  
pp. 263-278 ◽  
Author(s):  
Steven Alpern
Keyword(s):  
Weak Mixing

Is there large weak mixing in heavy nuclei?

1994 ◽  
Vol 49 (6) ◽  
pp. 3297-3300 ◽  
Author(s):  
J. J. Szymanski ◽  
J. D. Bowman ◽  
M. Leuschner ◽  
B. A. Brown ◽  
I. C. Girit
Keyword(s):  
Heavy Nuclei ◽  
Weak Mixing

scholarly journals FROM HADRONIC PARITY VIOLATION TO PARITY-VIOLATING ELECTRON SCATTERING AND TESTS OF THE STANDARD MODEL

2008 ◽  
Vol 23 (17n20) ◽  
pp. 1266-1277 ◽  
Author(s):  
WILLEM T. H. VAN OERS
Keyword(s):  
Standard Model ◽  
Electron Scattering ◽  
Parity Violation ◽  
New Physics ◽  
Theoretical Interpretation ◽  
Weak Mixing Angle ◽  
Weak Mixing ◽  
Mixing Angle ◽  
The Standard Model ◽  
Analyzing Power

Searches for parity violation in hadronic systems started soon after the evidence for parity violation in β-decay of 60 Co was presented by Madame Chien-Shiung Wu and in π and μ decay by Leon Lederman in 1957. The early searches for parity violation in hadronic systems did not reach the sensitivity required and only after technological advances in later years was parity violation unambiguously established. Within the meson-exchange description of the strong interaction, theory and experiment meet in a set of seven weak meson-nucleon coupling constants. Even today, after almost five decades, the determination of the seven weak meson-nucleon couplings is incomplete. Parity violation in nuclear systems is rather complex due to the intricacies of QCD. More straight forward in terms of interpretation are measurements of the proton-proton parity-violating analyzing power (normalized differences in scattering yields for positive and negative helicity incident beams), for which there exist three precision experiments (at 13.6, at 45, and 221 MeV). To-date, there are better possibilities for theoretical interpretation using effective field theory approaches. The situation with regard to the measurement of the parity-violating analyzing power or asymmetry in polarized electron scattering is quite different. Although the original measurements were intended to determine the electro-weak mixing angle, with the current knowledge of the electro-weak interaction and the great precision with which electro-weak radiative corrections can be calculated, the emphasis has been to study the structure of the nucleon, and in particular the strangeness content of the nucleon. A whole series of experiments (the SAMPLE experiment at MIT-Bates, the G0 experiment and HAPPEX experiments at Jefferson Laboratory (JLab), and the PVA4 experiment at MAMI) have indicated that the strange quark contributions to the charge and magnetization distributions of the nucleon are tiny. These measurements if extrapolated to zero degrees and zero momentum transfer have also provided a factor five improvement in the knowledge of the neutral weak couplings to the quarks. Choosing appropriate kinematics in parity-violating electron-proton scattering permits nucleon structure effects on the measured analyzing power to be precisely controlled. Consequently, a precise measurement of the ‘running’ of sin 2θw or the electro-weak mixing angle has become within reach. The [Formula: see text] experiment at Jefferson Laboratory is to measure this quantity to a precision of about 4%. This will either establish conformity with the Standard Model of quarks and leptons or point to New Physics as the Standard Model must be encompassed in a more general theory required, for instance, by a convergence of the three couplings (strong, electromagnetic, and weak) to a common value at the GUT scale. The upgrade of CEBAF at Jefferson Laboratory to 12 GeV, will allow a new measurement of sin 2θW in parity-violating electron-electron scattering with an improved precision to the current better measurement (the SLAC E158 experiment) of the ‘running’ of sin 2θW away from the Z0 pole. Preliminary design studies of such an experiment show that a precision comparable to the most precise individual measurements at the Z0 pole (to about ±0.00025) can be reached. The result of this experiment will be rather complementary to the [Formula: see text] experiment in terms of sensitivity to New Physics.

scholarly journals Weak-mixing implies sensitive dependence

2004 ◽  
Vol 299 (1) ◽  
pp. 300-304 ◽  
Author(s):  
Lianfa He ◽  
Xinhua Yan ◽  
Lingshu Wang
Keyword(s):  
Weak Mixing ◽  
Sensitive Dependence
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