
ISSN:
1930-5311
eISSN:
1930-532X
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Journal of Modern Dynamics
2018 , Volume 12
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We prove a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms. Our results are inspired by and analogous to recent results for diagonal quadratic forms due to Bourgain [
Using classical results of Rogers [
A celebrated result of Ratner from the eighties says that two horocycle flows on hyperbolic surfaces of finite area are either the same up to algebraic change of coordinates, or they have no non-trivial joinings. Recently, Mohammadi and Oh extended Ratner's theorem to horocycle flows on hyperbolic surfaces of infinite area but finite genus. In this paper, we present the first joining classification result of a horocycle flow on a hyperbolic surface of infinite genus: a $\mathbb{Z}$ or $\mathbb{Z}^2$-cover of a general compact hyperbolic surface.
In this paper we prove results on Birkhoff and Oseledets genericity along certain curves in the space of affine lattices and in moduli spaces of translation surfaces. In the space of affine lattices
In this paper, we prove that every graphical hypersurface in a prequantization bundle over a symplectic manifold
Let
We show that, for generic choices of
Let
We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.
We prove a conjecture of Viana which states that Lyapunov exponents vary continuously when restricted to
We construct an example of a Teichmüller geodesic ray whose limit set in the Thurston boundary of Teichmüller space is a
We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgo-pyat-type condition on nonexistence of approximate eigenfunctions, we prove that existing results for (possibly non-Markovian) nonuniformly expanding maps hold also for their toral extensions.
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