Whyburn’s conjecture for $C\sp{2}$ maps

Whyburn'S conjecture for some differentiable maps.

A bound for Feichtinger conjecture

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

Lang Maps and Harris’s Conjecture Preliminary Version

We work over fields of characteristic 0. Let X be a variety of general type defined over a number field K. A well known conjecture of S. Lang [L] states that the set of rational points X(K) is not Zariski dense in X. As noted in [א], this implies that if X is a variety which only dominates a variety of general type then X(K) is still not dense in X. J. Harris proposed a way to quantify this sit...

The Dynamical Mordell-lang Conjecture for Skew-linear Self-maps

Let k be an algebraically closed field of characteristic 0, let N ∈ N, let g : P−→P be a non-constant morphism, and let A : A−→A be a linear transformation defined over k(P), i.e., for a Zariski open dense subset U ⊂ P, we have that for x ∈ U(k), the specialization A(x) is an N -by-N matrix with entries in k. We let f : P×A99KP×A be the rational endomorphism given by (x, y) 7→ (g(x), A(x)y). We...

A Monotonicity Conjecture for Real Cubic Maps . 1

Section 2 sets the stage by describing the parameter triangle T for real cubic maps, either of shape + + or of shape + , and by describing basic properties of topological entropy. Section 3 describes the monotonicity problem for the topological entropy function, and states the Monotonicity Conjecture. Section 4 describes the family of stunted sawtooth maps, and proves the analogous conjecture f...