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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...
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...
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...
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 ...
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 ...
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...
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...
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...
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...
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...
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...
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...
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 procedure for constructing conservative numerical integra-tors for time dependent partial di erential equations is presented. In particular, linearly implicit methods preserving a time avera...

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