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Similarly, the second of equations (30) yields equation (32) and the inequality (33)with the tangent replaced by the minus cotangent.
For a given trajectory (that is, given the initial conditions at the source), the maximum possible fundamental occurs when the trajectory has a vertical tangent.
The concept of visible tangent links can be extended to arbitrary shaped obstacles.
The tangent vectors are scaled to a fixed length.
Instead of using the action on tangent vectors, we use the action on pairs of tangent vectors.
In particular, it will become important to show that their unit tangent vectors form a set of measure zero in the unit tangent bundle.
We will also need to compare tangent spaces at nearby points.
In order to make it competitive it must be combined with some other algorithm that reduces the number of tangent distance comparisons to make.
In this bifurcation the geometrical splitting of the tangent space is preserved but the expansion in the unstable direction degenerates near a periodic orbit.
The theoretical curves follow closely the dashed and dash-dotted numerical curves, and the abrupt change in tangent angle appears to fit almost exactly.
The metric g determines the isomorphism of the tangent and cotangent bundles.
One can see that the edge segments tangent to the circles intersected by each of these lines have a constant orientation.
The tangent is inclined downward, so the local effect of the magnetic field is stabilizing.
Theorem 3.6 covers the situation where all the sheets coincide, as opposed to merely being tangent.
By the unique integrability of these laminations, it is enough to deal with their tangent distributions.
