Ergodicity of typical billiards

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In summary, the conversation is about someone trying to find papers on a dramatic result regarding billiard systems becoming ergodic under typical perturbations. They mention names of potential authors and express difficulty in understanding the mathematical jargon in the papers. They also mention a book by Sergei Tabachnikov as a potential resource.
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deathprog23
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I'm trying to find the papers where a rather dramatic result on billiard systems was proved: for 'typical' perturbations away from an integrable billiard, the system becomes ergodic.

Even a paper mentioning such a result would be good start - all I have to go on at the moment are names given to me by the person who I heard the result from: Gutkin, Troubetzkoy and Markarian.

I've tried searching through their papers; but being a physicist, I get lost in the mathematical jargon.

No idea if this is a likely place to get help, but thanks if anyone can assist.
 
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Try Sergei Tabachnikov's 1995 book "Billiards": you can find a preprint here http://www.math.psu.edu/tabachni/Books/books.html
 

Related to Ergodicity of typical billiards

1. What is the concept of ergodicity in typical billiards?

Ergodicity is a mathematical concept that describes the behavior of a system over time. In the case of typical billiards, ergodicity refers to the idea that the motion of a billiard ball on a billiard table will eventually explore all possible positions on the table with equal probability.

2. How is the ergodicity of typical billiards related to chaos theory?

The ergodicity of typical billiards is closely related to chaos theory, which studies the behavior of dynamical systems that are highly sensitive to initial conditions. In a typical billiard system, the slightest change in the angle or speed of the ball can result in drastically different trajectories, making it a chaotic system.

3. What factors can affect the ergodicity of a billiard system?

Several factors can affect the ergodicity of a billiard system, including the shape and size of the table, the material of the table's surface, the initial conditions of the ball's movement, and any external forces acting on the ball (such as friction or air resistance).

4. How is the ergodicity of typical billiards studied and measured?

The ergodicity of typical billiards is typically studied and measured through computer simulations and mathematical models. These methods allow scientists to analyze the behavior of the system over time and make predictions about its ergodicity.

5. What real-world applications does the study of ergodicity in typical billiards have?

The study of ergodicity in typical billiards has applications in various fields, including physics, mathematics, and engineering. It can help scientists better understand the dynamics of chaotic systems and make predictions about the behavior of particles in other physical systems, such as gases or fluids.

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