Rational billiards and flat structures

By H. Masur, Serge Tabachnikov. 2002

389 citations recorded by the source corpus.

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Citations in the corpus

Geometry and billiards (2005, methodology): “Starting with [60], serious progress has been made in understanding the dynamics of rational polygonal billiards, using methods of complex analysis; see [65] for a survey of this subject.”
The field of definition of affine invariant submanifolds of the moduli space of abelian differentials (2012, methodology): “For an introduction to the field of translation surfaces, see the surveys by Masur and Tabachnikov [21] and Zorich [37].”
INFINITELY GENERATED VEECH GROUPS (2004, background): “It is a standard result, see say [ MT ], that the flow in a given direction is nonminimal only if the direction is the direction of some saddle connection.”
Characterizations of lattice surfaces (2008, methodology): “For more details we refer the reader to [ 12 , 23, 25].”
Dynamics and geometry of the Rauzy–Veech induction for quadratic differentials (2007, background): “[ MT02 ]). Thus Rn(T) is minimal and so is T.”
Teichmuller curves, triangle groups, and Lyapunov exponents (2005, background): “This part is independent of the previous sections, and requires only elementary notions of translation surfaces (see [23] or 2).”
Non-ergodic Z-periodic billiards and infinite translation surfaces (2011, methodology): “Using the unfolding process described in [33] (see for example [39]), one can verify that, for every direction θ ∈ S(1) the ow (bt )t∈R is isomorphic to the directional ow (φ̃t )t∈R on a non-compact translation surface (M̃, ω̃l), where (M̃, ω̃l) is the translation surface resulting from gluing, alon”
On groups generated by two positive multi-twists: Teichmuller curves and Lehmer's number (2003, background): “For more details on Teichmüller space and quadratic differentials see Gardiner and Lakic [23], Masur [40], Masur and Tabachnikov [41], Earle and Gardiner [17], and McMullen [44].”
Cylinder deformations in orbit closures of translation surfaces (2013, methodology): “Background For an introduction to translation surfaces, see the surveys by Masur and Tabachnikov [14] and Zorich [30].”
Euler characteristics of Teichmüller curves in genus two (2006, background): “Tabachnikov [51], Veech [76; 77; 78; 79], Kontsevich [42], Zorich [84], Möller [60], or Bouw and Möller [16].”