Applications over Complex Lagrangians

Complex Lagrangian mechanics with constraints

In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on it. If the form is closed, it is found that the constraint is (locally) holonomic. In the result, complex analogous of some topics in constrained Lagrangian mechanical system is concluded.

Unveiling the Fractal Structure of Julia Sets with Lagrangian Descriptors

In this paper we explore by means of the method of Lagrangian descriptors the Julia sets arising from complex maps, and we analyze their underlying dynamics. In particular, we take a look at two classical examples: the quadratic mapping $z_{n+1} = z^2_n + c$, and the maps generated by applying Newton's method to find the roots of complex polynomials. To achieve this goal, we provide an extension of this scalar diagnostic that is capable of revealing the phase space of open maps in the complex plane, allowing us to avoid potential issues of orbits escaping to infinity at an increasing rate. The…

Classification of Lagrangian Fibrations over a Klein Bottle

This paper completes the classification of regular Lagrangian fibratiopns over compact surfaces. \cite{misha} classifies regular Lagrangian fibrations over $\mathbb{T}^2$. The main theorem in \cite{hirsch} is used in order to classify integral affine structures on the Klein bottle $K^2$ and, hence, regular Lagrangian fibrations over this space.

功率变换器拉格朗日建模的一些贡献

Some contributions to Lagrangian modelling of Power Converters

本文提出了一种基于拉格朗日建模的系统化方法来推导复杂功率电子变换器的数学模型，首次将该方法扩展至标准电路的非理想高保真描述，简化了系统仿真与设计过程。