scholarly journals Multi-moment maps on nearly Kähler six-manifolds

2020 ◽  
Author(s):  
Giovanni Russo
Keyword(s):  
Fixed Points ◽  
Critical Points ◽  
Orbit Space ◽  
One Dimensional ◽  
Moment Maps ◽  
Trivalent Graph ◽  
Nearly Kähler

Abstract We study multi-moment maps on nearly Kähler six-manifolds with a two-torus symmetry. Critical points of these maps have non-trivial stabilisers. The configuration of fixed-points and one-dimensional orbits is worked out for generic six-manifolds equipped with an $$\mathrm {SU}(3)$$ SU ( 3 ) -structure admitting a two-torus symmetry. Projecting the subspaces obtained to the orbit space yields a trivalent graph. We illustrate this result concretely on the homogeneous nearly Kähler examples.

ONE-DIMENSIONAL CHAOS IN IMPULSED LINEAR OSCILLATING CIRCUITS

1993 ◽  
Vol 03 (04) ◽  
pp. 921-941 ◽  
Author(s):  
LAURA GARDINI ◽  
RENZO LUPINI
Keyword(s):  
Asymptotic Behavior ◽  
Fixed Points ◽  
Critical Point ◽  
Critical Points ◽  
Phase Plane ◽  
Global Bifurcation ◽  
Homoclinic Bifurcation ◽  
Combined Effect ◽  
Chaotic Oscillations ◽  
One Dimensional

The dynamics of a damped linear oscillating circuit subject to impulses is represented by a one-dimensional endomorphism (or noninvertible map) π: ℝ → ℝ. The asymptotic behavior of orbits in the phase-plane is characterized in terms of critical points and point singularities of π (fixed points or cycles). Their combined effect, that is, the merging of a critical point into a repelling cycle, causes a global bifurcation or a homoclinic bifurcation, with transition to chaotic oscillations.

scholarly journals Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points

2009 ◽  
Vol 102 (25) ◽  
Author(s):  
Frank Pollmann ◽  
Subroto Mukerjee ◽  
Ari M. Turner ◽  
Joel E. Moore
Keyword(s):  
Critical Points ◽  
Quantum Critical Points ◽  
One Dimensional ◽  
Quantum Critical

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

2022 ◽  
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Dynamic Characteristics ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Two Dimensional ◽  
Initial State ◽  
One Dimensional ◽  
Backward Euler ◽  
Short Period

Abstract The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

scholarly journals Toric Geometry of Spin(7)-Manifolds

2019 ◽  
Author(s):  
Thomas Bruun Madsen ◽  
Andrew Swann
Keyword(s):  
Symmetry Group ◽  
Orbit Space ◽  
Moment Map ◽  
Toric Geometry ◽  
Hamiltonian Action ◽  
Trivalent Graph ◽  
Dense Set

Abstract We study $ \operatorname{Spin}(7) $-manifolds with an effective multi-Hamiltonian action of a four-torus. On an open dense set, we provide a Gibbons–Hawking type ansatz that describes such geometries in terms of a symmetric $ 4\times 4 $-matrix of functions. This description leads to the 1st known $ \operatorname{Spin}(7) $-manifolds with a rank $ 4 $ symmetry group and full holonomy. We also show that the multi-moment map exhibits the full orbit space topologically as a smooth four-manifold, containing a trivalent graph in $ \mathbb{R}^4 $ as the image of the set of the special orbits.

scholarly journals Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model

2015 ◽  
Vol 92 (4) ◽  
Author(s):  
M. Dalmonte ◽  
W. Lechner ◽  
Zi Cai ◽  
M. Mattioli ◽  
A. M. Läuchli ◽  
...  
Keyword(s):  
Hubbard Model ◽  
Critical Points ◽  
Luttinger Liquids ◽  
One Dimensional ◽  
The One
Sign in / Sign up

Export Citation Format

Share Document