The Topology of Chaos: libtop man page

libtop(4) libtop(4)

NAME
libtop is a set of programs and a C++ library for doing computations
related to templates and knots, i.e. topological analysis (of low-
dimensional systems). This manual page describes the file formats used
by the programs and the library.

DESCRIPTION
Fiilleess ooff iinnvvaarriiaannttss
Many commands of the libtop package [see, e.g., _o_r_b_c_o_m_b(1) or _f_i_n_d_-
_n_a_m_e_s(1)] take as input a file listing topological invariants of
extracted periodic orbits. The contents of this file must be as fol-
lows.

n
slk1 trs1 per1 [SRRR_1 SRRR_2 SRRR_p1 ]
... ... ...
slkn trsn pern [SRRR_1 SRRR_2 SRRR_pn ]

n11 n12 lk(n11,n12) [RRR_11_12_1 RRR_11_12_2
RRR_11_12_l]
... ... ...
ni1 ni2 lk(ni1,ni2) [RRR_i1_i2_1 RRR_i1_i2_2
RRR_i1_i2_l]
... ... ...
* * *

- The first line indicates the number n of orbits. Only the first
string appearing on this line will be read.

- Each of the n following lines gives the self-linking number,
torsion, period of one orbit and, if available, (self-)relative
rotation rates. Orbits will be numbered 1..n according to their
order of appearance in this list. They are expected to be sorted
by increasing period (i.e., period-1 orbits come first). If the
torsion or the self-linking number of an orbit is not known (or
cannot be determined unambiguously), the joker character '*' can
be used instead.

If a line contains data beyond the first three strings, these
data are assumed to be the self-relative rotation rates of the
orbit mutiplied by the period. They should listed in the order
R11=0, R12, R13, ... where Rij is the rotation rate between
initial conditions #i and #j, numbered according to the order of
visit. For example, the line describing the period-4 orbit of
the horseshoe template should be

5 3 4 0 2 1 2

corresponding to a self-linking number of 5, a torsion of 3 and
a period of 4, and a set of RRR = [0,(1/2)^2,1/4].

- A blank line separates one-orbit invariants (self-linking num-
bers, period, and so on) from two-orbit invariants (linking num-
bers, relative rotation rates).

- Each line gives then the value of the linking number of orbits
whose numbers are indicated at the beginning of the line. Only
the first three strings of the line are read.

Where the value of an invariant is not available, an asterisk (*) can
be entered, except for periods which are mandatory. End of file is
indicated by a line with three asterisks.