As you can see in this image (and others in previous posts) all these orbits are bounded in a region of phase space. Whereas some of them have an extremely complicated unfolding, this is taking place in a very specific region without escaping. The underlying concept of this concentration of states consisting the orbit (chaotic or not) is that of the attractor. The attractor is part of the phase-space of a dynamical system, where its orbits converge. It can be a point (or points), a limit cycle, a surface, or a volume. Except from these cases, attractors may be much more complicated, like the one of the figure above. These complex types of attractor are called strange attractors. In strange attractors the concentration of orbits can be very dense, and their mathematical description requires the definition of a more generalized concept of dimension. Thus, the above structure, due to its complexity, corresponds to a strange attractor. Rendered with chaoscope
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As you can see in this image (and others in previous posts) all these orbits are bounded in a region of phase space. Whereas some of them have an extremely complicated unfolding, this is taking place in a very specific region without escaping. The underlying concept of this concentration of states consisting the orbit (chaotic or not) is that of the attractor.

The attractor is part of the phase-space of a dynamical system, where its orbits converge. It can be a point (or points), a limit cycle, a surface, or a volume.

Except from these cases, attractors may be much more complicated, like the one of the figure above. These complex types of attractor are called strange attractors. In strange attractors the concentration of orbits can be very dense, and their mathematical description requires the definition of a more generalized concept of dimension.

Thus, the above structure, due to its complexity, corresponds to a strange attractor.

Rendered with chaoscope

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