Symbolic codes for rotational orbits and “islands-around-islands” are constructed for the quadratic, area-preserving Hénon map. The codes are based upon continuation from an anti-integrable limit or, alternatively, from the horseshoe. Given any sequence of rotation numbers we obtain symbolic sequences for the corresponding elliptic and hyperbolic rotational orbits. These are shown to be consist...

It is shown that the usual first variational formula for the energy of a harmonic map (or equivariant harmonic map) with respect to the conformal structure on a two dimensional domain extends to case of nonpositively curved metric space targets. As applications, we recover Gardiner’s formula for the variation of the Hubbard-Masur differential and a proof of the existence and uniqueness of quadr...

The quadratic iteration is mapped using a nondistributive real scator algebra in three dimensions. The bound set S has a rich fractal-like boundary. Periodic points on the scalar axis are necessarily surrounded by off axis divergent magnitude points. There is a one-to-one correspondence of this set with the bifurcation diagram of the logistic map. The three-dimensional S set exhibits selfsimila...

It is shown that in a controlled adiabatic homotopy between two Hamiltonians, H0 and H1, the gap or “anti-crossing” phenomenon can be viewed as the development of cusps and swallow tails in the region of the complex plane where two critical value curves of the quadratic map associated with the numerical range of H0 + iH1 come close. The “near crossing” in the energy level plots happens to be a ...

The quadratizations of a (homogeneous nonquadratic) nonlinear polynomial system of ODEs introduced by Myung and Sagle in [17] is considered. The 1-1 correspondence between homogeneous quadratic systems of ODEs and nonassociative algebras is used to prove a special structure of the algebra corresponding to a general homogeneous quadratic systems being a quadratization. Every homogeneous solution...

Estimating the most likely configuration (MAP) is one of the fundamental tasks in probabilistic models. While MAP inference is typically intractable for many real-world applications, linear programming relaxations have been proven very effective. Dual block-coordinate descent methods are among the most efficient solvers, however, they are prone to get stuck in sub-optimal points. Although subgr...

Abstract We discuss the singularity structure of Kahan discretizations a class quadratic vector fields and provide classification parameter values such that corresponding map is integrable, in particular, admits an invariant pencil elliptic curves.

In this paper generation of binary sequences derived from chaotic sequences defined over Z4 is proposed. The six chaotic map equations considered in this paper are Logistic map, Tent Map, Cubic Map, Quadratic Map and Bernoulli Map. Using these chaotic map equations, sequences over Z4 are generated which are converted to binary sequences using polynomial mapping. Segments of sequences of differe...

Given a Sobolev homeomorphism f ? W 2,1 in the plane we find piecewise quadratic that approximates it up to set of ? measure. We show this map can be approximated by diffeomorphisms norm on set.

We compute the domain of existence of two-dimensional invariant tori with fixed frequency vectors for a fourdimensional, complex, symplectic map. The map is a generalization of the semi-standard map studied by Greene and Percival; it has three parameters, a, and a, representing the strength of the kicks in each degree of freedom, and E, the coupling. The domain of existence of a torus in (a,, a...