Monotone twist maps and Dowker-type theorems

Generalized quadrangles and generalized polygons in finite geometry (51E12) Convex sets in (2) dimensions (including convex curves) (52A10) Dynamical aspects of twist maps (37E40) Dynamical systems with singularities (billiards, etc.) (37C83)

Cites Work

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Computing Mather's $\beta$-function for Birkhoff billiards
Degenerate billiards
Spectral invariants of convex planar regions
Polygonal approximation of plane convex bodies
Equivalence of glancing hyper-surfaces
The geometry of circumscribing polygons of minimal perimeter
Asymptotic approximation of convex curves
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Degenerate billiards in celestial mechanics
The principle of least action in geometry and dynamics
On the dual billiard problem
Area-length duality and the characteristic 2-chain
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Symplectically convex and symplectically star-shaped curves: a variational problem
Wire billiards, the first steps
On the regularity of Mather's $\beta$-function for standard-like twist maps
Perimeter approximation of convex discs in the hyperbolic plane and on the sphere
Dual billiards
Homology groups of relations
Symplectic twist maps. Global variational techniques
Algebraic non-integrability of magnetic billiards
Approximation to Plane Convex Curves. (I) Dowker-Type Theorems
Symplectic maps, variational principles, and transport
Classical billiards in magnetic fields
Lagrangian relations and linear point billiards
On minimum circumscribed polygons
The geometry of Minkowski spaces -- a survey. I
Higher order terms of Mather's $\beta$-function for symplectic and outer billiards