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ENTROPY OF COUPLED MAP LATTICES     Coupled map lattice  Pesin formula  Ruelle inequality       font style='font-size:12px;'> 2015/9/29
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...
FINITE-SIDED DEFORMATION SPACES OF COMPLETE AFFINE 3-MANIFOLDS     3-MANIFOLDS  DEFORMATION SPACES       font style='font-size:12px;'> 2015/9/29
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...
Stretching Three-Holed Spheres and the Margulis Invariant     Margulis Invariant  Three-Holed Spheres       font style='font-size:12px;'> 2015/9/29
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...
ACTION OF THE JOHNSON-TORELLI GROUP ON REPRESENTATION VARIETIES     JOHNSON-TORELLI  mapping class group       font style='font-size:12px;'> 2015/9/29
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...
ERGODICITY OF MAPPING CLASS GROUP ACTIONS ON SU(2)-CHARACTER VAR IET IES     GROUP ACTIONS  MAPPING CLASS       font style='font-size:12px;'> 2015/9/29
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.
Affine Schottky Groups and Crooked Tilings     Affi  ne Schottky Groups  Crooked Tilings       font style='font-size:12px;'> 2015/9/29
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...
THE RADIANCE OBSTRUCTION AND PARALLEL FORMS ON AFFINE MANIFOLDS     RADIANCE OBSTRUCTION  PARALLEL FORMS       font style='font-size:12px;'> 2015/9/29
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...
Three-Dimensional Affine Crystallographic Groupd     Affine Crystallographic Groupd  affine       font style='font-size:12px;'> 2015/9/29
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       font style='font-size:12px;'> 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...
Afflne manilolds with nilpotent holonomy     nilpotent holonomy  affine       font style='font-size:12px;'> 2015/9/29
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...
Dense Orbits for Abelian Affine Groups      affine action  dense  orbit  group  abelian  transitive       font style='font-size:12px;'> 2011/2/24
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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