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A numerical study of infinitely renormalizable area-preserving maps
renormalizable area-preserving maps numerical study Dynamical Systems
2011/9/14
Abstract: It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equa...
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Bounded Variation Piecewise Area Preserving Maps Dynamical Systems
2011/8/30
Abstract: We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewis...
Strong-Stability-Preserving, K-Step, 5- to 10-Stage, Hermite-Birkhoff Time-Discretizations of Order 12
Strong Stability Preserving, Hermite-Birkhoff Method SSP Coefficient Time Discretization Method of Lines Comparison with Other SSP Methods
2013/1/30
We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of ord...
Annular area preserving homeomorphisms which admit no interior compact invariant sets
Area preserving homeomorphisms rotation numbers fast approxi-mation by conjugation
2011/2/28
For any irrational number , there exists an ergodic area preserv-ing homeomorphism of the closed annulus which is isotopic to the identitity,admits no compact invariant set contained in the interior ...
Symmetry preserving self-adjoint extensions of Schrödinger operators with singular potentials
Symmetry preserving self-adjoint extensions Schrö dinger operators singular potentials
2011/1/21
We develop a general technique for finding self-adjoint extensions of a symmetric operator that respect a given set of its symmetries. Prob-lems of this type naturally arise when considering two- and ...
Lorentz-preserving fields in Lorentz-violating theories
Lorentz-preserving fields Lorentz-violating theories
2010/12/23
We identify a fairly general class of field configurations (of spins 0, 1/2 and 1) which preserve Lorentz invariance in effective field theories of Lorentz violation characterized by a constant timel...
The lattice structure of connection preserving deformations for q-Painleve equations I
Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/10
We wish to explore a link between the Lax integrability of the q-Painleve equations and the symmetries of the q-Painleve equations. To do this, we consider the set of associated linear problems for th...
Higher order Painleve system of type D^{(1)}_{2n+2} and monodromy preserving deformation
Painleve system monodromy preserving deformation
2010/11/8
The higher order Painleve system of type D^{(1)}_{2n+2} is proposed by Y. Sasano. It is an extension of the sixth Painleve equation for the affine Weyl group symmetry and expressed as a Hamiltonian sy...
Graphene as a quantum surface with curvature-strain preserving dynamics
Graphene preserving dynamics
2010/11/19
We discuss how the curvature and the strain density of the atomic lattice generate the quantization of graphene sheets as well as the dynamics of geometric quasiparticles propagating along the constan...
On positive definite preserving linear transformations of rank $r$ on real symmetric matrices
positive definite linear transformations
2010/11/22
We study on what conditions on $B_k,$ \ a linear transformation of rank $r$ \label{form} T(A)=\sum_{k=1}^r\tr(AB_k)U_k where $U_k,\ k=1,2,..., r$ are linear independent and all positive definite; is p...
Free Products and the Lack of State Preserving Approximations of Nuclear C*-algebras
Free Products Nuclear C*-algebras
2010/11/17
Let $A$ be a homogeneous C*-algebra and $\phi$ a state on $A.$ We show that if $\phi$ satisfies a certain faithfulness condition, then there is a net of finite-rank, unital completely positive, $\phi...
We consider systems of ordinary differential equations with known first integrals. The notion of a discrete tangent space is introduced as the orthogonal complement of an arbitrary set of discrete gr...
Polarization-preserving confocal microscope for optical experiments in a dilution refrigerator with high magnetic field
Polarization-preserving confocal microscope optical experiments dilution refrigerator magnetic field
2010/11/11
We present the design and operation of a fiber-based cryogenic confocal microscope. It is designed as a compact cold-finger that fits inside the bore of a superconducting magnet, and which is a modula...
Period Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping Principle
Period Doubling Renormalization Area-Preserving Maps Mild Computer Assistance
2010/11/29
A universal period doubling cascade analogous to the famous Feigenbaum-Coullet-Tresser period doubling has been observed in area-preserving maps of R2. Existence of the “universal” map with orbits of ...
A general framework for deriving integral preserving numerical methods for PDEs
general framework deriving integral preserving numerical methods PDEs
2010/12/8
A general procedure for constructing conservative numerical integra-tors for time dependent partial dierential equations is presented. In particular, linearly implicit methods preserving a time avera...