Lorenz and Intermittent Maps

Runs and plots the intermittent map and lorenz like map

lorenzlikemap.m
% Part 1 runs and plots the 1D Lorenz-like map with parameters beta, theta and
% alpha for t time steps where the Lorenz-like map is the following:
% T(x) = theta*(abs(x-0.5)^alpha) for x in [0, 1/2) and
% T(x) = 1-theta*(abs(x-0.5)^alpha) for x in [1/2,1]
% Part 2 runs and plots the 2D Lorenz map where F(x,y) = (T(x),G(x,y))
% Outputs one plot of both maps, vector x corresponding to
% T(x),T^2(x)... and 2 by t array corresponding to F(x,y)
% This map was taken from the paper:
% Rigorous Computation of Invariant Measures and Fractal Dimension for
% Piecewise Hyperbolic Maps: 2D Lorenz Like maps, Galatolo, Nisoli, arXiv:
% 1402.5918v1
function [x, F] = lorenzlikemap(beta,theta,alpha,t)
intermittentmap.m
% Runs and plots the intermittent map where T(x) = x*(1+2^alpha*x^alpha)
% when x is in [0,1/2) and T(x) = 2*x-1 when x is in [1/2,1]
% The output vector x corresponds the the vector: x, T(x), T^2(x),...
% the input parameters are alpha and number of time steps t.

function [x] = intermittentmap(alpha,t)

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It is important to note that with these functions it is simple to create and view different observables on each of the maps with a few more lines of code.

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