Recursion Operators and Frobenius Manifolds

Primary Invariants of Hurwitz Frobenius Manifolds

It is a classical result that flat coordinates for a Hurwitz Frobenius manifold can be obtained as periods of a differential along cycles on the domain curve. We generalise this construction to primary invariants of the Hurwitz Frobenius manifolds. We show that they can be obtained as periods of multidifferentials along the same cycles. The multidifferentials are obtained via the topological re...

Frobenius Manifolds as a Special Class of Submanifolds in Pseudo-Euclidean Spaces

We introduce a very natural class of potential submanifolds in pseudo-Euclidean spaces (each Ndimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudoEuclidean space) and prove that each N-dimensional Frobenius manifold can be locally represented as an N-dimensional potential submanifold. We show that all potential submanifolds bear natural special ...

Weighted Frobenius-Perron and Koopman operators

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.