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The entropy of coupled map lattices with respect to the group of space-time translations is considered. We use the notion of generalized Lyapunov spectra ([11]) to prove the analogue of Ruelle inequ...
Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs).
An important discovery of the 20th century mathematics is that many deterministic systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
A natural family of affine cubic surfaces arises from SL(2)-characters of the 4-holed sphere and the 1-holed torus. The ideal locus is a tritangent plane which is generic in the sense that the...
A Margulis spacetime is a complete affine 3-manifold M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S. We show that eve...
This paper applies the authors’ forthcoming work, ”Affine deformations of a three-holed sphere” in Lorentzian geometry to prove a result in hyperbolic geometry. Namely, an infinitesimal de...
Let Σ be a compact orientable surface with genus g and n boundary components B = (B1,...,Bn). Let c = (c1,...,cn) ∈ [−2,2]n. Then the mapping class group MCG of Σ acts on the relative SU(2)-cha...
Let be a compact orientable surface with genus g andnboundary components ∂1,..., ∂n. Let b = (b1,...,bn) ∈ [−2,2] n. Then the mapping class group Mod() acts on the relative SU(2)-...
When G is a connected compact Lie group, and π is a closed surface group, then Hom(π, G)/G contains an open dense Out(π)-invariant subset which is a smooth symplectic manifold.
In his doctoral thesis [3] and subsequent papers [4, 5], Todd Drumm developed a theory of fundamental domains for discrete groups of isometries of Minkowski (2 + 1)-space E, using polyhedra called c...
A manifold M is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine. When they are locally linear M is called radiant. The obstruction to radiance is a o...
Those groups r which act properly discontinuously and aillnely on II?’ with compact fundamental domain are classified. First it is shown that such a group f contains a solvable subgroup of finite ...
TWO EXAMPLES OF AFFINE MANIFOLDS     AFFINE MANIFOLDS  affine       2015/9/29
An affine manifold is a manifold with a distinguished system of affine coordinates, namely, an open covering by charts which map homeomorphically onto open sets in an affine space E such that on ov...
An affine manifold is a differentiable manifold together with an atlas of coordinate charts whose coordinate changes extend to affine automorphisms of Euclidean space. These charts are called atli...
In this paper, we give a characterization of existence of a dense orbit for the action on Cn of an abelian affine subgroup G of GA(n,C). We prove in particular that if G has a dense orbit then the clo...

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