Chaos Attractor: +inf as Attractor?

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SUMMARY

The discussion centers on the concept of +inf as an attractor in dynamical systems, particularly in relation to trajectories in state space. It is established that points outside the Mandelbrot set are indeed attracted to infinity, confirming that +inf can be considered an attractor for certain maps. This conclusion is supported by the behavior of trajectories emanating from various initial conditions in the state space.

PREREQUISITES
  • Understanding of dynamical systems theory
  • Familiarity with the Mandelbrot set and its properties
  • Knowledge of attractors and their significance in mathematical maps
  • Basic concepts of state space in mathematics
NEXT STEPS
  • Explore the properties of the Mandelbrot set in greater detail
  • Research the implications of attractors in chaotic systems
  • Study the mathematical definitions and examples of state space
  • Investigate other types of attractors beyond +inf
USEFUL FOR

Mathematicians, physicists, and anyone interested in chaos theory and dynamical systems will benefit from this discussion, particularly those exploring the behavior of trajectories in complex maps.

Shobhit Gupta
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Can we consider +inf as an attractor for a map for which trajectories emanating from any point in the state space tends to +inf.
 
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Certainly. The points outside the Mandelbrot set are "attracted to infinity".
 

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