M | A | T | H |

2 | 1 | B |

Mathematics Math21b Spring 2007

Linear Algebra and Differential Equations

Exhibit: lilac bush

Course Head: Oliver Knill

Office: SciCtr 434

Email: knill@math.harvard.edu

Bretschers book discusses on page 305 the growth of a lilac bush
If x(n) is the number of new branches and y(n) is the number of old branches
and initially, we have 1 new branch, we want to see how the bush grows
if every new branch becomes an old branch in the next step and every old
branch additionally grows two new branches. The dynamical system is
given by the matrix A with eigenvalues v1,v2 and eigenvalues l1,l2
A = | 0 2 | | 1 1 |It has the eigenvalues 2 and -1 and the eigenbasis v1= | 1 | v2 = | -2 | | 1 | | 1 | |

Please send questions and comments to math21b@fas.harvard.edu

Math21b | Oliver Knill | Spring 2007 |
Department of Mathematics |
Faculty of Art and Sciences |
Harvard University