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ENTROPY OF COUPLED MAP LATTICES
Coupled map lattice Pesin formula Ruelle inequality
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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...
THE DIFFUSION COEFFICIENT FOR PIECEWISE EXPANDING MAPS OF THE INTERVAL WITH METASTABLE STATES
DIFFUSION COEFFICIENT WITH METASTABLE STATES
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2015/9/29
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).
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
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2015/9/29
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...
AFFINE CUBIC SURFACES AND RELATIVE SL(2)-CHARACTER VARIETIES OF COMPACT SURFACES
AFFINE CUBIC SURFACES RELATIVE SL(2)-CHARACTER
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2015/9/29
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
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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
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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
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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
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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)-...
THE MAPPING CLASS GROUP ACTS REDUCIBLY ON SU(n)-CHARACTER VARIETIES
CLASS GROUP ACTS REDUCIBLY VARIETIES
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2015/9/29
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
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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
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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
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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
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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
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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
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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...