Supercyclic C0-semigroups, stability and somewhere dense orbits

2019 ◽  
Vol 476 (2) ◽  
pp. 539-548 ◽  
Author(s):  
Abhay Kumar ◽  
Sachi Srivastava
Keyword(s):  
Dense Orbits

Bratteli–Vershik models for partial actions of ℤ

2017 ◽  
Vol 28 (10) ◽  
pp. 1750073 ◽  
Author(s):  
Thierry Giordano ◽  
Daniel Gonçalves ◽  
Charles Starling
Keyword(s):  
Cantor Set ◽  
Bratteli Diagram ◽  
Partial Action ◽  
Dense Orbits

Let [Formula: see text] and [Formula: see text] be open subsets of the Cantor set with nonempty disjoint complements, and let [Formula: see text] be a homeomorphism with dense orbits. Building on the ideas of Herman, Putnam and Skau, we show that the partial action induced by [Formula: see text] can be realized as the Vershik map on an ordered Bratteli diagram, and that any two such diagrams are equivalent.

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 Isometric Group Actions on Hilbert Spaces: Structure of Orbits

2008 ◽  
Vol 60 (5) ◽  
pp. 1001-1009 ◽  
Author(s):  
Yves de Cornulier ◽  
Romain Tessera ◽  
Alain Valette
Keyword(s):  
Hilbert Space ◽  
Nilpotent Group ◽  
Hilbert Spaces ◽  
Metabelian Group ◽  
Isometric Action ◽  
Finitely Generated ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Isometric Group Actions ◽  
Dense Orbits

AbstractOur main result is that a finitely generated nilpotent group has no isometric action on an infinite-dimensional Hilbert space with dense orbits. In contrast, we construct such an action with a finitely generated metabelian group.

Simultaneous dense and non-dense orbits for certain partially hyperbolic diffeomorphisms

2018 ◽  
Vol 40 (4) ◽  
pp. 1083-1107
Author(s):  
WEISHENG WU
Keyword(s):  
Hausdorff Dimension ◽  
Tangent Space ◽  
Anosov Diffeomorphism ◽  
Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Dense Orbits ◽  
Set Of Points ◽  
Partially Hyperbolic Diffeomorphism ◽  
Stable Subspace

Let$g:M\rightarrow M$be a$C^{1+\unicode[STIX]{x1D6FC}}$-partially hyperbolic diffeomorphism preserving an ergodic normalized volume on$M$. We show that, if$f:M\rightarrow M$is a$C^{1+\unicode[STIX]{x1D6FC}}$-Anosov diffeomorphism such that the stable subspaces of$f$and$g$span the whole tangent space at some point on$M$, the set of points that equidistribute under$g$but have non-dense orbits under$f$has full Hausdorff dimension. The same result is also obtained when$M$is the torus and$f$is a toral endomorphism whose center-stable subspace does not contain the stable subspace of$g$at some point.

Dense orbits of critical points for the tent map

1991 ◽  
pp. 57-61 ◽  
Author(s):  
K. M. Brucks ◽  
B. Diamond ◽  
M. V. Otero-Espinar ◽  
C. Tresser
Keyword(s):  
Critical Points ◽  
Tent Map ◽  
Dense Orbits

scholarly journals Dense orbits of rationals

1993 ◽  
Vol 117 (4) ◽  
pp. 1201-1201 ◽  
Author(s):  
Michael D. Boshernitzan
Keyword(s):  
Dense Orbits

scholarly journals Linear semigroups with coarsely dense orbits

2014 ◽  
Vol 200 (1) ◽  
pp. 327-341
Author(s):  
H. Abels ◽  
A. Manoussos
Keyword(s):  
Dense Orbits
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