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It is shown that a countable symmetric multiplicative subgroup $G=-Hcup H$ with $Hsubsetmathbb{R}_+^ast$ is the group of self-similarities of a Gaussian-Kronecker flow if and only if $H$ is additively $mathbb{Q}$-independent. In particular, a real number $s eqpm1$ is a scale of self-similarity of a Gaussian-Kronecker flow if and only if $s$ is transcendental. We also show that each countable symmetric subgroup of $mathbb{R}^ast$ can be realized as the group of self-similarities of a simple spectrum Gaussian flow having the Foias-Stratila property.
In this paper, directional sequence entropy and directional Kronecker algebra for $mathbb{Z}^q$-systems are introduced. The relation between sequence entropy and directional sequence entropy are established. Meanwhile, direcitonal discrete spectrum s
Similarity solutions play an important role in many fields of science: we consider here similarity in stochastic dynamics. Important issues are not only the existence of stochastic similarity, but also whether a similarity solution is dynamically att
We show that the horocycle flow associated with a foliation on a compact manifold by hyperbolic surfaces is minimal under certain conditions.
The Seifert Conjecture asks, Does every non-singular vector field on the 3-sphere ${mathbb S}^3$ have a periodic orbit? In a celebrated work, Krystyna Kuperberg gave a construction of a smooth aperiodic vector field on a plug, which is then used to c
We establish various analogs of the Kronecker-Weyl equidistribution theorem that can be considered higher-dimension