Ergodicity of typical billiards

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SUMMARY

The discussion centers on the ergodicity of typical billiard systems, specifically how perturbations from integrable billiards lead to ergodic behavior. Key figures mentioned include Gutkin, Troubetzkoy, and Markarian, who have contributed to this area of research. A recommended resource is Sergei Tabachnikov's 1995 book "Billiards," which provides foundational insights and can be accessed via a preprint link. This discussion highlights the intersection of physics and mathematics in understanding complex dynamical systems.

PREREQUISITES
  • Understanding of ergodic theory
  • Familiarity with billiard dynamics
  • Basic knowledge of mathematical jargon used in physics
  • Access to academic papers and preprints
NEXT STEPS
  • Read Sergei Tabachnikov's 1995 book "Billiards" for foundational concepts
  • Research the works of Gutkin, Troubetzkoy, and Markarian on billiard systems
  • Explore ergodic theory applications in dynamical systems
  • Investigate typical perturbations in mathematical physics
USEFUL FOR

Physicists, mathematicians, and researchers interested in dynamical systems, particularly those studying the ergodic properties of billiard systems and their perturbations.

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
 

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