We construct 9-parameter and 13-parameter dynamical systems of the plane which map bi-quadratic curves to other bi-quadratic curves and return to the original curve after two iterations. These generalize the QRT maps which map each such curve to itself. The new families of maps include those that were found as reductions of integrable lattices by [11].

In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or "eruption," is described. A fundamental role is played by the interactions of fixed points and singular curves. Other critical elements in the phase space include periodic points and an invariant line. The dynamics along the invariant lin...

It is shown that if f is a mapping of the plane onto itself that is uniformly continuous with modulus of continuity Ω(r) which is o( √ r) as r → 0 and f is also co-uniformly continuous then f = P ◦ h where h is a homeomorphism of the plane and P is a complex polynomial. The same conclusion holds also under other assumptions on the moduli of uniform and co-uniform continuity. However, we also pr...

The perceptual correlates of sensory cyclofusion have received little attention. However, they are easily elicited by asking patients with torsion about perceived slant of the visual world, and by watching how they hold the Titmus or Randot book. Sensory cyclofusion induces two types of perceptual aberrations. First, it rotates the plane of maximal stereoscopic volume in the pitch plane. As suc...

The Half-Plane Half-Comb walk is a random on the plane, when we have square lattice upper half-plane and comb structure lower half-plane, i.e., horizontal lines below x-axis are removed. We prove that probability this returns to origin in 2N steps asymptotically equal $$2/(\pi N).$$ 2 / ( ? N ) . As consequence, strong laws limit distribution for local time.

We consider problems concerning the existence of solutions Beltrami equations and their convergence in complex plane. are mainly interested case when these satisfy so-called hydrodynamic normalization condition neighborhood infinity. Under some conditions on dilatations inverse mappings, we have established such class continuous Sobolev mappings. also obtained results locally uniform limit a se...

Under identical viewing conditions, observers made two types of judgement about the shape of stereoscopically defined surfaces: one required an estimate of viewing distance for correct performance (e.g. setting the depth of a hemi-cylinder to equal its half-height or a dihedral angle to 90 deg), the other did not (matching the depth of, for example, sinusoidal corrugations or hemi-cylinders pre...