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Topic: **Systems/Dynamical systems**

You are looking at all articles with the topic **"Systems/Dynamical systems"**. We found 3 matches.

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# ðŸ”— Interplanetary Transport Network

The **Interplanetary Transport Network** (**ITN**) is a collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow. The ITN makes particular use of Lagrange points as locations where trajectories through space are redirected using little or no energy. These points have the peculiar property of allowing objects to orbit around them, despite lacking an object to orbit. While it would use little energy, transport along the network would take a long time.

### Discussed on

- "Interplanetary Transport Network" | 2014-11-08 | 98 Upvotes 18 Comments

# ðŸ”— PoincarÃ© Recurrence Theorem

In mathematics and physics, the **PoincarÃ© recurrence theorem** states that certain dynamical systems will, after a sufficiently long but finite time, return to a state arbitrarily close to (for continuous state systems), or exactly the same as (for discrete state systems), their initial state.

The **PoincarÃ© recurrence time** is the length of time elapsed until the recurrence. This time may vary greatly depending on the exact initial state and required degree of closeness. The result applies to isolated mechanical systems subject to some constraints, e.g., all particles must be bound to a finite volume. The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics. Systems to which the PoincarÃ© recurrence theorem applies are called conservative systems.

The theorem is named after Henri PoincarÃ©, who discussed it in 1890 and proved by Constantin CarathÃ©odory using measure theory in 1919.

### Discussed on

- "PoincarÃ© Recurrence Theorem" | 2024-01-28 | 57 Upvotes 30 Comments

# ðŸ”— Abelian sandpile model

The **Abelian sandpile model**, also known as the **Bakâ€“Tangâ€“Wiesenfeld model**, was the first discovered example of a dynamical system displaying self-organized criticality. It was introduced by Per Bak, Chao Tang and Kurt Wiesenfeld in a 1987 paper.

The model is a cellular automaton. In its original formulation, each site on a finite grid has an associated value that corresponds to the slope of the pile. This slope builds up as "grains of sand" (or "chips") are randomly placed onto the pile, until the slope exceeds a specific threshold value at which time that site collapses transferring sand into the adjacent sites, increasing their slope. Bak, Tang, and Wiesenfeld considered process of successive random placement of sand grains on the grid; each such placement of sand at a particular site may have no effect, or it may cause a cascading reaction that will affect many sites.

The model has since been studied on the infinite lattice, on other (non-square) lattices, and on arbitrary graphs (including directed multigraphs). It is closely related to the dollar game, a variant of the chip-firing game introduced by Biggs.

### Discussed on

- "Abelian sandpile model" | 2018-08-31 | 66 Upvotes 5 Comments