This paper throws light on chaotic shift keying-based speech encryption and decryption method. In this method, the input speech signals are sampled and its values are segmented into four levels, namely L0, L1, L2, and L3. Each level of sampled values is permuted using four chaotic generators such as logistic map, tent map, quadratic map, and Bernoulli’s map. A chaotic shift keying mechanism ass...

Suppose E/F is a quadratic extension of number fields and GU(2, 2) is the quasi-split unitary similitude group attached to E/F . We prove functoriality from globally generic cuspidal representations of GU(2, 2)(AF ) to automorphic representations of GL6(AF ) corresponding to the twisted exterior square map on the dual side. For a split quadratic algebra E/F , the twisted exterior square map red...

We deene the Farey web | a collection of loci in the parameter plane of families of simple non-invertible maps of the circle. We prove some results about the arrangement of these loci and their relationships with other dynamically signiicant features of the parameter plane. The results enable us to provide short proofs for a number of theorems about the organization of frequency-locking. Figure...

We study the linear map, AZ(p) : TpE 2 → TpE associated with the linearization of a planar flow with tangent vector field Z. A quadratic form constructed from this map contains information about the expansion of the flow in an arbitrary direction and its eigenvectors represent directions of maximum and minimum expansion. A second quadratic form provides information about the rotation of the flo...

We prove the Regulat or Stochastic Conjecture for the real quadratic family which asserts that almost every real quadratic map Pc, c in [-2, 1/4], has either an attracting cycle or an absolutely continuous invariant measure.

Let f(x) = ax+bx+c ∈ Z[x] be a quadratic polynomial with a ̸≡ 0 mod p. Take z ∈ Fp and let Oz = {fi(z)}i∈Z+ be the orbit of z under f , where fi(z) = f(fi−1(z)) and f0(z) = z. For M < |Oz|, We study the diameter of the partial orbit OM = {z, f(z), f2(z), . . . , fM−1(z)} and prove that there exists c1 > 0 such that diam OM & min { Mp c1 , 1 log p M 4 5p 1 5 ,M 1 13 log logM } . For a complete or...

For an ideal I of O(D), we will denote its image in the ideal class monoid by [I]. In particular, composing the map f 7→ I(f) with the map which sends an ideal to its class, we get a map which sends a primitive, positive definite quadratic form f of discriminant D to the ideal class [I(f)]. This has remarkable properties. Indeed, we have the following important and beautiful result (unlike some...

We prove that almost every real quadratic map is either regular or Collet-Eckmann. This implies exponential rates of mixing of the last renormalization of the map. We also show that the recurrence of the critical orbit is polynomial in a full measure set. It follows from a result of Baladi and Viana that almost every quadratic map is stochastically stable in the strong sense. Combined with meth...