scholarly journals A one dimensional manifold is of cohomological dimension $2$

1975 ◽  
Vol 52 (1) ◽  
pp. 445-445
Author(s):  
Satya Deo
Keyword(s):  
Cohomological Dimension ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
Dimension 2

A group with zero homology

1968 ◽  
Vol 64 (3) ◽  
pp. 599-602 ◽  
Author(s):  
D. B. A Epstein
Keyword(s):  
Fundamental Group ◽  
Cohomological Dimension ◽  
Dimensional Manifold ◽  
Finitely Generated ◽  
3 Dimensional ◽  
Identity Group ◽  
Dimension 2

In this paper we describe a group G such that for any simple coefficients A and for any i > 0, Hi(G; A) and Hi(G; A) are zero. Other groups with this property have been found by Baumslag and Gruenberg (1). The group G in this paper has cohomological dimension 2 (that is Hi(G; A) = 0 for any i > 2 and any G-module A). G is the fundamental group of an open aspherical 3-dimensional manifold L, and is not finitely generated. The only non-trivial part of this paper is to prove that the fundamental group of the 3-manifold L, which we shall construct, is not the identity group.

SIMPLE AND COMPLEX DYNAMICS FOR ONE-DIMENSIONAL MANIFOLD MAPS

1995 ◽  
Vol 05 (05) ◽  
pp. 1351-1355
Author(s):  
VLADIMIR FEDORENKO
Keyword(s):  
Topological Entropy ◽  
Complex Dynamics ◽  
Periodic Points ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
Circle Maps ◽  
Interval Maps ◽  
Chain Recurrent Set ◽  
Recurrent Set

We give a characterization of complex and simple interval maps and circle maps (in the sense of positive or zero topological entropy respectively), formulated in terms of the description of the dynamics of the map on its chain recurrent set. We also describe the behavior of complex maps on their periodic points.

Computation of 2D Manifold Based on Generalized Condition

2012 ◽  
Vol 580 ◽  
pp. 210-213
Author(s):  
Zhong Wu ◽  
Meng Jia ◽  
Qing Hua Ji
Keyword(s):  
Dimensional Manifold ◽  
One Dimensional ◽  
Prediction Scheme ◽  
Accuracy Criterion

The new algorithm uses the idea of growing the manifold. The preimage of the new point is found quickly with a method called gradient prediction scheme and a new accuracy criterion is proposed. Furthermore, our algorithm is capable of computing both stable and unstable one dimensional manifold.

scholarly journals The Gross–Pitaevskii Equation with a Nonlocal Interaction in a Semiclassical Approximation on a Curve

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 201
Author(s):  
Alexander V. Shapovalov ◽  
Anton E. Kulagin ◽  
Andrey Yu. Trifonov
Keyword(s):  
Linear Equation ◽  
Semiclassical Approximation ◽  
Nonlocal Interaction ◽  
Pitaevskii Equation ◽  
Dimensional Manifold ◽  
Complex Germ ◽  
One Dimensional ◽  
The Cauchy Problem ◽  
Symmetry Operators ◽  
Interaction Term

We propose an approach to constructing semiclassical solutions for the generalized multidimensional Gross–Pitaevskii equation with a nonlocal interaction term. The key property of the solutions is that they are concentrated on a one-dimensional manifold (curve) that evolves over time. The approach reduces the Cauchy problem for the nonlocal Gross–Pitaevskii equation to a similar problem for the associated linear equation. The geometric properties of the resulting solutions are related to Maslov’s complex germ, and the symmetry operators of the associated linear equation lead to the approximation of the symmetry operators for the nonlocal Gross–Pitaevskii equation.

TRANSITIONAL DYNAMICS AND THRESHOLDS IN ROMER'S ENDOGENOUS TECHNOLOGICAL CHANGE MODEL

2002 ◽  
Vol 6 (3) ◽  
pp. 442-456 ◽  
Author(s):  
Pedro Garcia-Castrillo ◽  
Marcos Sanso
Keyword(s):  
Steady State ◽  
Technological Change ◽  
Dynamic Behavior ◽  
Physical Capital ◽  
Change Model ◽  
Dimensional Manifold ◽  
Transitional Dynamics ◽  
One Dimensional ◽  
Endogenous Technological Change ◽  
Relevant Variables

We obtain the transitional dynamics of the decentralized economy described by P.M. Romer and characterize the dynamic behavior of the most relevant variables. We determine the existence of a stable one-dimensional manifold containing a steady state with innovation, unique in ratios, and also find a threshold in the accumulation of physical capital below which the economy is not innovating. Finally, using simulations, we assess the significance of this threshold and analyze the influence that technological and utility parameters have on it.

PERIODIC ORBITS NEAR A HETEROCLINIC LOOP FORMED BY ONE-DIMENSIONAL ORBIT AND A TWO-DIMENSIONAL MANIFOLD: APPLICATION TO THE CHARGED COLLINEAR THREE-BODY PROBLEM

2007 ◽  
Vol 17 (06) ◽  
pp. 2175-2183
Author(s):  
JAUME LLIBRE ◽  
DANIEL PAŞCA
Keyword(s):  
Periodic Orbits ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Negative Energy ◽  
Dimensional Manifold ◽  
Three Body Problem ◽  
Heteroclinic Loop ◽  
One Dimensional ◽  
Three Body ◽  
Total Collision

This paper is devoted to the study of a type of differential systems which appear usually in the study of the Hamiltonian systems with two degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near to the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear three-body problem.

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