Wikipedia's definition of a dynamical system

In summary, there is a general definition of dynamical systems found on Scholarpedia and "Introduction to the Modern Theory of Dynamical Systems" by Katok and Hasselblatt is recommended as a useful reference book for those studying this topic.
  • #1
phibonacci
6
0
Hi,

In http://en.wikipedia.org/wiki/Dynamical_system_%28definition%29" dynamical systems are defined in a very general way. Does anyone know a book that contains this definition? I didn't find it in any of the books in the reference list of the Wikipedia article. I am writing a text that focuses on discrete dynamical systems, but I would still like to include the general definition, and therefore I need a reliable source I can refer to.

Thanks in advance,

phibonacci
 
Last edited by a moderator:
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  • #3
Thanks for the tip. I also found "Introduction to the Modern Theory of Dynamical Systems" by Katok and Hasselblatt to be quite useful.
 

FAQ: Wikipedia's definition of a dynamical system

What is the definition of a dynamical system according to Wikipedia?

According to Wikipedia, a dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. It involves studying the behavior of a system over time and the factors that influence its evolution.

What is the difference between a discrete and continuous dynamical system?

A discrete dynamical system involves changes that occur in a fixed sequence of time steps, while a continuous dynamical system involves changes that occur continuously over time. In other words, a discrete system is represented by a set of distinct points, while a continuous system is represented by a smooth curve.

What are the key components of a dynamical system?

The key components of a dynamical system include the state space, which represents all possible states of the system, the time evolution function, which describes how the system changes over time, and the initial conditions, which specify the starting state of the system.

How are dynamical systems used in real-world applications?

Dynamical systems have various applications in fields such as physics, biology, economics, and engineering. They can be used to model and predict the behavior of complex systems, such as weather patterns, population dynamics, and traffic flow.

What are some common types of dynamical systems?

Some common types of dynamical systems include linear systems, chaotic systems, and nonlinear systems. Linear systems involve simple, predictable behavior, while chaotic systems exhibit complex, unpredictable behavior. Nonlinear systems involve interactions between multiple variables and can exhibit a mix of linear and chaotic behavior.

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