scholarly journals Topological transitivity and wandering intervals for group actions on the line $\mathbb R$

2018 ◽  
Vol 13 (1) ◽  
pp. 293-307
Author(s):  
Enhui Shi ◽  
Lizhen Zhou
Keyword(s):  
Group Actions ◽  
Topological Transitivity

scholarly journals Topological transitivity of solvable group actions on the line R

2009 ◽  
Vol 116 (2) ◽  
pp. 203-215 ◽  
Author(s):  
Suhua Wang ◽  
Enhui Shi ◽  
Lizhen Zhou ◽  
Grant Cairns
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Topological Transitivity

scholarly journals Topological Transitivity and Mixing Notions for Group Actions

2007 ◽  
Vol 37 (2) ◽  
pp. 371-397 ◽  
Author(s):  
Grant Cairns ◽  
Alla Kolganova ◽  
Anthony Nielsen
Keyword(s):  
Group Actions ◽  
Topological Transitivity

TOPOLOGICAL TRANSITIVITY AND CHAOS OF GROUP ACTIONS ON DENDRITES

2009 ◽  
Vol 19 (12) ◽  
pp. 4165-4174 ◽  
Author(s):  
SUHUA WANG ◽  
ENHUI SHI ◽  
LIZHEN ZHOU ◽  
XUNLI SU
Keyword(s):  
Nilpotent Group ◽  
Group Action ◽  
Group Actions ◽  
Finitely Generated ◽  
Topological Transitivity ◽  
Ping Pong ◽  
Weakly Mixing

We show that each weakly mixing group action on a dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, we prove that no nilpotent group action on a dendrite is weakly mixing. At last, we show that each dendrite admits no chaotic group actions.

Li-York Chaos of Set-Valued Discrete Dynamical Systems Based on Semi-Group Actions

2013 ◽  
Vol 380-384 ◽  
pp. 1778-1782
Author(s):  
Yun Qian ◽  
Peng Guan
Keyword(s):  
Dynamical Systems ◽  
Periodic Point ◽  
Metric Space ◽  
Hausdorff Metric ◽  
Group Actions ◽  
Discrete Dynamical Systems ◽  
Semi Group ◽  
Topological Transitivity ◽  
Hausdorff Metric Space

t is well known that a semi-groups action on a space could appear chaos phenomenon, like Li-York chaos and so on. Li-York chaos has important relations with topological transitivity and periodic point. This study analyzed metric space and its dinduced Hausdorff metric space. Letis a semi-group. We make continuously act on space. We study topological transitivity and betweenand. Some important results are presented which show that if is topological transitivity and periodicity (which means Li-York chaos at the same time), then the action of semi-grouponis Li-York chaos.

Disjoint topological transitivity for weighted translations generated by group actions

2021 ◽  
Vol 71 (5) ◽  
pp. 1229-1240
Author(s):  
Chung-Chuan Chen ◽  
Seyyed Mohammad Tabatabaie ◽  
Ali Mohammadi
Keyword(s):  
Group Actions ◽  
Group Element ◽  
Necessary Condition ◽  
Compact Groups ◽  
Topological Transitivity ◽  
Locally Compact ◽  
Topological Mixing ◽  
Quotient Spaces ◽  
Sufficient And Necessary Condition

Abstract In this note, we give a sufficient and necessary condition for weighted translations, generated by group actions, to be disjoint topologically transitive in terms of the weights, the group element and the measure. The characterization of disjoint topological mixing is obtained as well. Moreover, we apply the results to the quotient spaces of locally compact groups and hypergroups.

Generating pairs and group actions

2014 ◽  
Vol 218 (5) ◽  
pp. 777-783
Author(s):  
Darryl McCullough
Keyword(s):  
Group Actions

scholarly journals The close relation between border and Pommaret marked bases

2021 ◽  
Author(s):  
Cristina Bertone ◽  
Francesca Cioffi
Keyword(s):  
Finite Order ◽  
Polynomial Ring ◽  
Group Actions ◽  
Close Relation ◽  
Open Covering ◽  
Order Ideal ◽  
Lower Dimension ◽  
Hilbert Schemes ◽  
Affine Spaces ◽  
The Ideal

AbstractGiven a finite order ideal $${\mathcal {O}}$$ O in the polynomial ring $$K[x_1,\ldots , x_n]$$ K [ x 1 , … , x n ] over a field K, let $$\partial {\mathcal {O}}$$ ∂ O be the border of $${\mathcal {O}}$$ O and $${\mathcal {P}}_{\mathcal {O}}$$ P O the Pommaret basis of the ideal generated by the terms outside $${\mathcal {O}}$$ O . In the framework of reduction structures introduced by Ceria, Mora, Roggero in 2019, we investigate relations among $$\partial {\mathcal {O}}$$ ∂ O -marked sets (resp. bases) and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked sets (resp. bases). We prove that a $$\partial {\mathcal {O}}$$ ∂ O -marked set B is a marked basis if and only if the $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked set P contained in B is a marked basis and generates the same ideal as B. Using a functorial description of these marked bases, as a byproduct we obtain that the affine schemes respectively parameterizing $$\partial {\mathcal {O}}$$ ∂ O -marked bases and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked bases are isomorphic. We are able to describe this isomorphism as a projection that can be explicitly constructed without the use of Gröbner elimination techniques. In particular, we obtain a straightforward embedding of border schemes in affine spaces of lower dimension. Furthermore, we observe that Pommaret marked schemes give an open covering of Hilbert schemes parameterizing 0-dimensional schemes without any group actions. Several examples are given throughout the paper.

scholarly journals On some kinds of dense orbits in general nonautonomous dynamical systems

2020 ◽  
Vol 7 (1) ◽  
pp. 163-175
Author(s):  
Mehdi Pourbarat
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Point Of View ◽  
Topological Conjugacy ◽  
Topological Transitivity ◽  
Nonautonomous Systems ◽  
Nonautonomous Dynamical Systems ◽  
Sensitive Dependence ◽  
Dense Orbits

AbstractWe study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.

scholarly journals Schottky groups acting on homogeneous rational manifolds

2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Picard Group ◽  
Schottky Group ◽  
Fundamental Groups ◽  
Complex Manifolds ◽  
Schottky Groups ◽  
Algebraic Dimension ◽  
Geometric Invariants ◽  
Compact Complex Manifolds

AbstractWe systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of {{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.

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