Continuous Limit of Discrete Sawtooth Maps and its Algebraic Framework

Quantum Dynamical Entropies and Complexity in Dynamical Systems

We analyze the behaviour of two quantum dynamical entropies in connection with the classical limit. Using strongly chaotic classical dynamical systems as models (Arnold Cat Maps and Sawtooth Maps), we also propose a discretization procedure that resembles quantization; even in this case, studies of quantum dynamical entropy production are carried out and the connection with the continuous limit is explored. In both case (quantization and discretization) the entropy production converge to the Kolmogorov-Sinai invariant on time-scales that are logarithmic in the quantization (discretization) par…

Algebraic Entropy of Birational Maps with Invariant Curves

The relevance of the algebraic entropy in the study of birational discrete time dynamical systems highlights the need to relate it to other characteristics of these systems. In this letter, two complementary proofs are given that the foliation of the space by invariant curves implies that the algebraic entropy is zero.

An Algebraic Characterization of Vacuum States in Minkowski Space. III. Reflection Maps

Employing the algebraic framework of local quantum physics, vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables and corresponding state a continuous unitary representation of the proper Poincare group which acts covariantly on the net and leaves the state invariant. The present results and methods substantially improve upon previous work. In particular, the continuity properties of the representation are shown to be a consequence of the net structure, and surmised cohom…

Stäckel系统的Miura映射

Miura maps for Stäckel systems

本文通过定义超椭圆型参数依赖代数曲线间的Miura映射，诱导出Stäckel系统间的Miura映射，从而为Stäckel系统生成多哈密顿表示提供了新途径。

参数反射映射：一种代数方法

Parametric reflection maps: an algebraic approach

本文提出了一种基于参数(p)-shelves和racks的代数方法，用于研究参数集合论反射方程的解，并引入了新的代数结构以简化约束条件。

Algebraic Birkhoff Factorization and the Euler-Maclaurin Formula on Cones

We equip the space of lattice cones with a coproduct which makes it a connected cograded colagebra. The exponential sum and exponential integral on lattice cones can be viewed as linear maps on this space with values in the space of meromorphic germs with linear poles at zero. We investigate the subdivision properties-- reminiscent of the inclusion-exclusion principle for the cardinal on finite sets-- of such linear maps and establish a compatibility of these properties with respect to the convolution quotient of the coalgebra. Implementing the Algebraic Birkhoff Factorization procedure on the…