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Effects of nondenumerable fixed points in finite dynamical systems
Sagar Chakraborty1, J K Bhattacharjee
1S.N. Bose National Center for Basic Sciences, Salt Lake, Kolkata 700098, India. sagar@bose.res.in
Chaos (Woodbury, N.Y.)
|April 2, 2008
Summary
A spinning soccer ball
Area of Science:
- Physics
- Dynamical Systems Theory
Background:
- Traditional dynamical systems define fixed points as static states.
- The motion of a spinning soccer ball challenges this traditional definition.
Purpose of the Study:
- To explore the existence of evolving fixed points in finite dynamical systems.
- To re-evaluate the chaotic nature of a free-kicked soccer ball's motion.
Main Methods:
- Analysis of the dynamics of a spinning object in a phase space.
- Theoretical consideration of systems with a nondenumerably infinite number of fixed points.
Main Results:
- Identified a class of finite dynamical systems with potentially infinite, evolving fixed points.
- Demonstrated that fixed points in these systems are not permanent.
Conclusions:
- The traditional concept of a fixed point may not apply to all dynamical systems.
- A free-kicked soccer ball's motion can be considered nonchaotic under these new considerations.
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