scholarly journals $C^1$-differentiable conjugacy of Anosov diffeomorphisms on three dimensional torus

2008 ◽  
Vol 22 (1/2, September) ◽  
pp. 183-200 ◽  
Author(s):  
Misha Guysinsky ◽  
Andrey Gogolev
Keyword(s):  
Three Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphisms

On the integrability of intermediate distributions for Anosov diffeomorphisms

1995 ◽  
Vol 15 (2) ◽  
pp. 317-331 ◽  
Author(s):  
M. Jiang ◽  
Ya B. Pesin ◽  
R. de la Llave
Keyword(s):  
Finite Number ◽  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphism ◽  
Anosov Diffeomorphisms ◽  
Stable Foliation

AbstractWe study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.

Arithmetical theory of Anosov diffeomorphisms

1987 ◽  
Vol 413 (1844) ◽  
pp. 97-107 ◽  
Keyword(s):  
Nineteenth Century ◽  
Periodic Orbits ◽  
Algebraic Number ◽  
Number Fields ◽  
Dynamical Behaviour ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Algebraic Number Fields ◽  
Anosov Diffeomorphisms ◽  
The Way

Nineteenth century arithmetic is used to study periodic orbits of Anosov diffeomorphisms of the two-dimensional torus. We find that the period of the orbits, as well as their dynamical behaviour, are intimately related to the way ideals factorize in algebraic number fields.

Asymptotic estimate for the counting problems corresponding to the dynamical system on some decorated graphs

2017 ◽  
Vol 38 (5) ◽  
pp. 1697-1708 ◽  
Author(s):  
V. L. CHERNYSHEV ◽  
A. A. TOLCHENNIKOV
Keyword(s):  
Dynamical System ◽  
Wave Packet ◽  
General Theorem ◽  
Three Dimensional ◽  
Initial Time ◽  
Dimensional Torus ◽  
Counting Problems ◽  
One Dimensional ◽  
Moving Points ◽  
Narrow Wave

We study a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds, that is, a decorated graph. We consider the following dynamical system on decorated graphs. Suppose that, at the initial time, we have a narrow wave packet on a one-dimensional edge. It can be thought of as a point moving along the edge. When a packet arrives at the point of gluing, the expanding wavefront begins to spread on the Riemannian manifold. At the same time, there is a partial reflection of the wave packet. When the wavefront that propagates on the surface comes to another point of gluing, it generates a reflected wavefront and a wave packet on an edge. We study the number of Gaussian packets, that is, moving points on one-dimensional edges as time goes to infinity. We prove the asymptotic estimations for this number for the following decorated graphs: a cylinder with an interval, a two-dimensional torus with an interval and a three-dimensional torus with an interval. Also we prove a general theorem about a manifold with an interval and apply it to the case of a uniformly secure manifold.

scholarly journals Broadcastings and digit tilings on three-dimensional torus networks

2011 ◽  
Vol 412 (4-5) ◽  
pp. 307-319 ◽  
Author(s):  
Ryotaro Okazaki ◽  
Hirotaka Ono ◽  
Taizo Sadahiro ◽  
Masafumi Yamashita
Keyword(s):  
Three Dimensional ◽  
Dimensional Torus ◽  
Torus Networks

scholarly journals Regular variation and rates of mixing for infinite measure preserving almost Anosov diffeomorphisms

2018 ◽  
Vol 40 (3) ◽  
pp. 663-698 ◽  
Author(s):  
HENK BRUIN ◽  
DALIA TERHESIU
Keyword(s):  
Regular Variation ◽  
Return Time ◽  
Main Task ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphisms ◽  
Infinite Measure ◽  
Mixing Rates ◽  
First Return Time ◽  
Almost Anosov

The purpose of this paper is to establish mixing rates for infinite measure preserving almost Anosov diffeomorphisms on the two-dimensional torus. The main task is to establish regular variation of the tails of the first return time to the complement of a neighbourhood of the neutral fixed point.

Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical Generators

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Nataliya V. Stankevich ◽  
Natalya A. Shchegoleva ◽  
Igor R. Sataev ◽  
Alexander P. Kuznetsov
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Parameter Plane ◽  
Poincare Section ◽  
Dimensional Torus ◽  
Typical Structure ◽  
Periodic Oscillations ◽  
Torus Breakdown ◽  
Periodic Dynamics

Abstract Using an example a system of two coupled generators of quasi-periodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero, and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involves saddle tori occurring at their doublings. This transition is associated with typical structure of parameter plane, like cross-road area and shrimp-shaped structures, based on the two-frequency quasi-periodic dynamics. Using double Poincaré section, we have shown destruction of three-frequency torus.

Improving the performance of global communication on a three-dimensional torus network

1996 ◽  
Vol 27 (6) ◽  
pp. 24-32
Author(s):  
Yasushi Kawakura ◽  
Noboru Tanabe ◽  
Shigeru Oyanagi
Keyword(s):  
Three Dimensional ◽  
Global Communication ◽  
Dimensional Torus ◽  
Torus Network
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