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We define Ptolemy coordinates for representations that are not necessarily
boundary-unipotent. This gives rise to a new algorithm for computing the SL(2; C) Apolynomial, and more generally the ...
We give an e
ient simpli
ial formula for the volume and ChernSimons invariant of a boundary-paraboli
PSL(2,C)representation of a tame
3manifold
An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along
the leaves of this ...
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
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...
Stretching Three-Holed Spheres and the Margulis Invariant
Margulis Invariant Three-Holed Spheres
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...
The Margulis Invariant of Isometric Actions on Minkowski (2+1)-Space
Minkowski (2+1)-Space Isometric Actions
2015/9/29
Let E denote an a±ne space modelled on Minkowski (2+1)-space E
and let ¡ be a group of isometries whose linear part L(¡) is a purely hyperbolic
subgroup of SO0
(2;1). Margulis has deˉned ...
Invariant functions on Lie groups and Hamiltonian flows ofsurface group representations
Lie groups Hamiltonian flows
2015/9/29
In [7] it wasshown that ifn isthe fundamental group ofa closed oriented surface S
and Gis Lie group satisfying very general conditions, then the space Hom(n, G)/G
of conjugacy classes of representat...
DESTRUCTION OF INVARIANT CURVES IN THE RESTRICTED CIRCULAR PLANAR THREE-BODY PROBLEM BY USING COMPARISON OF ACTION
INVARIANT CURVES RESTRICTED CIRCULAR PLANAR THREE-BODY PROBLEM
2015/9/25
The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle al...
Normally hyperbolic invariant manifolds near strong double resonance
hyperbolic invariant manifolds near strong double resonance
2015/9/25
Normally hyperbolic invariant manifolds near strong double resonance.
Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances
Hyperbolic Invariant Laminations generalized Arnold away from resonances
2015/9/25
In this paper we study existence of Normally Hyperbolic Invariant Laminations (NHIL) for a nearly integrable system given by the product of the pendulum and the rotator perturbed with a small coupling...
NEW EXAMPLES OF S-UNIMODAL MAPS WITH A SIGMA-FINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURE
S-UNIMODAL MAPS SIGMA-FINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURE
2015/9/25
We combine the technique of inducing with a method of Johnson boxes and construct new examples of S-unimodal maps ϕ which do not have a finite absolutely continuous invariant measure, but do have...
Arnold diffusion in arbitrary degrees of freedom and crumpled 3-dimensional normally hyperbolic invariant cylinders
Arnold diffusion arbitrary degrees of freedom crumpled 3-dimensional hyperbolic invariant cylinders
2015/9/25
Arnold diffusion in arbitrary degrees of freedom and crumpled 3-dimensional normally hyperbolic invariant cylinders.
The unbounded dead end depth property is not a group invariant
group invariant depth property
2015/8/26
The dead-end depth of an element g of a group with finite generating set A is the distance from g to the complement of the radius d(1,g) closed ball, in the word metric d. We exhibit a finitely presen...
Probability on Groups: Random Walks and Invariant Diffusions
Invariant Diffusions Random Walks
2015/8/26
What do card shuffling, volume
growth, and Harnack inequalities
have to do with each other? They all
arise in the study of random walks
on groups. Probability on groups is
concerned with probabil...
Linked Solenoid Mappings and the Non-Transversality Locus Invariant
Solenoid Mappings Non-Transversality Locus Invariant
2015/8/26
Linked Solenoid Mappings and the Non-Transversality Locus Invariant.