Understanding Dynamical Systems: Questions on Terminology and Notation

[zetafunction]

I have some questions about dynamical system

- What do you call a 'flow' ?? , are you referring to the operator $$\sigma ^{t} =e^{itH}$$ with 'H' being a Hamiltonian operator

- In Deninger paper (see link below) it appears the definition 'Let be $$R_{p}$$ the R-vector space of real valued finite Fourier series on $$R/(logp)Z$$ , what is exactly the definition of the quotient space $$R/(logp)Z$$

the work by Deninguer can be foud here:

http://www.google.es/url?sa=t&sourc...yPyOAQ&usg=AFQjCNE3cXuK0vlsfXOFzhpxsSWMPTS0ew

 

[jvicens]

I can provide some clarification on these questions about dynamical systems.

Firstly, a 'flow' in dynamical systems refers to the evolution of a system over time. It is often represented by a vector field that describes the direction and speed at which the system moves in each point of its state space. This can be visualized as a flow of particles or fluid through the system.

Secondly, the operator \sigma ^{t} =e^{itH} is indeed related to dynamical systems, specifically to Hamiltonian systems. It is known as the time evolution operator and it describes how the system evolves over time based on its Hamiltonian, which is a mathematical function that represents the energy of the system.

Regarding the definition of the quotient space R/(logp)Z , this is a mathematical concept that is used to describe a space that is obtained by taking a larger space and "modding out" certain elements. In this case, it appears that the quotient space is being used to describe a space of real valued finite Fourier series on R/(logp)Z , which means that the elements of the space are functions that are periodic with period logp and have real values. The exact definition of this space may vary depending on the context in which it is used.

I hope this helps to clarify some of your questions about dynamical systems. If you have any further questions or need more information, please don't hesitate to ask. I am always happy to share my knowledge and expertise.