Communication: HK propagator uniformized along a one-dimensional manifold in weakly anharmonic systems

2014 ◽  
Vol 141 (18) ◽  
pp. 181102 ◽  
Author(s):  
Lucas Kocia ◽  
Eric J. Heller
Keyword(s):  
Dimensional Manifold ◽  
One Dimensional

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.

Workspace Analysis of Multibody Mechanical Systems Using Continuation Methods

1988 ◽  
Author(s):  
D.-Y. Jo ◽  
E. J. Haug
Keyword(s):  
Mechanical Systems ◽  
Point Of View ◽  
Continuation Methods ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
Generalized Coordinates ◽  
Workspace Analysis ◽  
Manifold Mapping ◽  
Manifold Theory

Abstract A new approach to numerical analysis of workspaces of multibody mechanical systems is developed. Numerical techniques that are based on manifold theory and utilize continuation methods are presented and applied to a variety of mechanical systems, including closed-loop mechanisms. Generalized coordinates that define kinematics of a system are classified and interpreted from an input-output point of view. Boundaries of workspaces, which depend on the classification of generalized coordinates, are defined as sets of singular points of Jacobians of the kinematic equations. Numerical methods for tracing one dimensional trajectories on a workspace boundary are outlined and example are analyzed using one dimensional manifold mapping computer programs, such as PITCON and AUTO.

Heat Kernel Expansions in the Case of Conic Singularities

2003 ◽  
Vol 18 (12) ◽  
pp. 2197-2203 ◽  
Author(s):  
R. Seeley
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Zeta Function ◽  
Differential Operators ◽  
Smooth Boundary ◽  
General Nature ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
The Third ◽  
Elliptic Differential Operators

For positive elliptic differential operators Δ, the asymptotic expansion of the heat trace tr(e-tΔ) and its related zeta function ζ(s, Δ) = tr(Δ-s) have numerous applications in geometry and physics. This article discusses the general nature of the boundary conditions that must be considered when there is a singular stratum, and presents three examples in which a choice of boundary conditions at the singularity must be made. The first example concerns the signature operator on a manifold with a singular stratum of conic type. The second concerns the "Zaremba problem" for a nonsingular manifold with smooth boundary, posing Dirichlet conditions on part of the boundary and Neumann conditions on the complement; the intersection of these two regions can be viewed as a singular stratum of conic type, and a boundary condition must be imposed along this stratum. The third example is a one-dimensional manifold where the operator at one end has a singularity like that in conic problems, and the choice of boundary conditions affects not just the residues at the poles of the zeta function, but also the very location of the poles

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