## Matlab Programs in connection with the paper:

### C^m Eigenfunctions of Perron-Frobenius Operators and a New Approach

### to Numerical Computation of Hausdorff Dimension: Applications in R^1

The following programs are used to compute the Hausdorff dimension
of the Cantor set E_{a_1, a_2,...,a_R} consisting of all points x
in the interval (0,1) with the continued fraction expansion:

x = [a_1, a_2, a_3, ..., a_R] = 1
----------------------
a_1 + 1
--------
a_2 + 1
---------
a_3 + ...

where each a_n is a positive integer.
hd1dP1i.m This is the main program for approximation
by continuous piecewise linear functions.

mat1d.m A program used by hd1dP1i.m

hd1dPni.m This is the main program for approximation
by continuous piecewise polynomials of degree <= n.

eval1dPn.m A program used by hd1dPni.m

thetabx.m A program used by hd1dP1i.m and
hd1dPni.m

The following programs are used to compute the Hausdorff dimension of the
invariant set obtained from iterations of the mappings:

theta_1(x) = (1/(3+2*lam))*x*(1 + lam*x*x*sqrt(x))

theta_2(x) = (1/(3+2*lam))*x*(1 + lam*x*x*sqrt(x)) + (2+lam)/(3+2*lam)

where 0 <= lam <= 1.

The choice lam =0 corresponds to the middle thirds Cantor set, whose
Hausdorff dimension is ln 2/ln 3.
hd1dperti.m The main program.

mat1dpert.m A program used by hd1dperti.m

thetabxlam.m A program used by hd1dperti.m

## Matlab Programs in connection with the paper:

### A New Approach to Numerical Computation of Hausdorff Dimension

### of Iterated Function Systems: Applications to Complex Continued Fractions

The following programs are used to compute the Hausdorff dimension of several
invariant sets in two dimensions.

For each of these problems, theta_b(z) = 1/(z+b) and z = x + iy belongs to

H:= {(x,y) in R^2: (x-1/2)^2 + y^2 <= 1/4, y >=0}.
The sets are:

I_1 = {b=m+ni: m is a positive integer and n an integer},

I_2 = {b=m-ni: m and n are positive integers},

I_3 = {b=m+ni: m = 1 and 2 and n = 0, 1, 2, -1,-2}.

hd2di.m The main program for the computation of
the Hausdorff dimension of the three sets

given above using piecewise bilinear functions.

matas.m A program used by hd2di.m

thetabz.m A program used by hd2di.m,
hd2dPni.m, and hd2dPnse.m.

kindx.m A program used by matas.m.

hd2dPni.m The main program for the computation of
the Hausdorff dimension of the set I_3

given above using higher order piecewise polynomials.

eval2dPni.m A program used by hd2dPni.m.

hd2dPnse.m Computation of the Hausdorff dimension
of a special example where the exact solution is known.

eval2dPnse.m A program used by hd2dPnse.m.