scholarly journals Algebraic dynamics of skew-linear self-maps

2018 ◽  
Vol 146 (10) ◽  
pp. 4369-4387 ◽  
Author(s):  
Dragos Ghioca ◽  
Junyi Xie
Keyword(s):  
Algebraic Dynamics

Algebraic dynamic study of geometric phase for a homonuclear linear spincluster

2007 ◽  
Vol 85 (8) ◽  
pp. 879-885
Author(s):  
X -X Chen ◽  
J Xue
Keyword(s):  
Magnetic Field ◽  
Coupling Strength ◽  
Geometric Phase ◽  
Time Dependent ◽  
Algebraic Dynamics ◽  
Spin Cluster ◽  
Alternative Expression ◽  
Linear Formula ◽  
External Time ◽  
The Magnetic Field

A homonuclear linear [Formula: see text] coupling spin cluster with the middle particle driven by an external time-dependent magnetic field is investigated by using the method of algebraic dynamics. The exact analytical solutions of the time-dependent Schrodinger equation of the spin cluster system are derived and employed to study the geometric phase. An alternative expression of the geometric phase in each eigenstate is obtained. It is shown that the geometric phase is related to the external magnetic-field parameter θ (the angle between the magnetic field and the Z axis) and the effective coupling strength Jn. Based on the relation, how the geometric phase depends on the coupling strength Jn in different reducible subspace is discussed.PACS Nos.: 33.20.Wr, 03.65.Fd, 03.65.Vf

scholarly journals Algebraic dynamics solution and algebraic dynamics algorithm of Burgers equations

2008 ◽  
Vol 51 (11) ◽  
pp. 1647-1652 ◽  
Author(s):  
Hua Zhang ◽  
WeiTao Lu ◽  
ShunJin Wang
Keyword(s):  
Algebraic Dynamics ◽  
Burgers Equations

Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Algebraic Geometry ◽  
Model Theory ◽  
Stability Theory ◽  
Analytic Geometry ◽  
Previous Knowledge ◽  
Real Numbers ◽  
Algebraic Dynamics ◽  
Theoretic Foundations ◽  
Rational Polytope ◽  
Deformation Retraction

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed and model-theoretic prerequisites are reviewed in the first sections.

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