The concept of a dynamical system has its origins in Newtonian mechanics. There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is an implicit relation that gives the state of the … See more

Many people regard French mathematician Henri Poincaré as the founder of dynamical systems. Poincaré published two now classical monographs, "New Methods of … See more

The concept of evolution in time is central to the theory of dynamical systems as seen in the previous sections: the basic reason for this fact is … See more

Linear dynamical systems can be solved in terms of simple functions and the behavior of all orbits classified. In a linear system the phase … See more

In the most general sense, a dynamical system is a tuple (T, X, Φ) where T is a monoid, written additively, X is a non-empty set and Φ is a function
$${\displaystyle \Phi :U\subseteq (T\times X)\to X}$$
with See more

• Arnold's cat map
• Baker's map is an example of a chaotic piecewise linear map
• Billiards and outer billiards
• Bouncing ball dynamics See more

The qualitative properties of dynamical systems do not change under a smooth change of coordinates (this is sometimes taken as a definition of qualitative): a singular point of the vector field (a point where v(x) = 0) will remain a singular point under smooth … See more