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math.SG2000
An obstruction to conservation of volume in contact dynamics
Leonid Polterovich
A theorem of Moser guarantees that every diffeomorphism of a closed manifold can be isotoped to a volume preserving one. We show that this statement cannot be extended into contact…
math.DS2000
Stable mixing for cat maps and quasi-morphisms of the modular group
Leonid Polterovich, Zeev Rudnick
It is well-known that the action of a hyperbolic element (``cat map'') of the modular group on the 2-torus has strong chaotic dynamical properties such as mixing and exponential de…