A new proof technique establishes ergodicity for anti-symmetric skew products over symmetric IETs with non-logarithmic singularities and enables analysis of error terms in Birkhoff sums for locally Hamiltonian flows with non-perfect saddles.
Zorich,How do the leaves of a closed1-form wind around a surface?Pseudoperiodic topology, 135–178
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On the ergodicity of anti-symmetric skew products with singularities and its applications
A new proof technique establishes ergodicity for anti-symmetric skew products over symmetric IETs with non-logarithmic singularities and enables analysis of error terms in Birkhoff sums for locally Hamiltonian flows with non-perfect saddles.