By Eli Maor, Eugen Jost

If you've ever idea that arithmetic and artwork don't combine, this gorgeous visible heritage of geometry will swap your brain. As a lot a piece of paintings as a booklet approximately arithmetic, *Beautiful Geometry* provides greater than sixty beautiful colour plates illustrating a variety of geometric styles and theorems, observed via short debts of the attention-grabbing heritage and other people in the back of every one. With art by means of Swiss artist Eugen Jost and textual content via acclaimed math historian Eli Maor, this designated occasion of geometry covers a number of matters, from straightedge-and-compass buildings to fascinating configurations regarding infinity. the result's a pleasant and informative illustrated travel during the 2,500-year-old background of 1 of an important and gorgeous branches of arithmetic.

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**Example text**

Denoting the evolution maps corresponding to Fµ , and F˜µ , by µ , respectively ˜ µ , whenever µ ({x} × [0, t]) ⊂ U , the homeomorphism H , or the homeomorphisms H1 and h, satisfy: ˜ h(µ) (H1 (x, µ), t) = H1 ( µ (x, t), µ). A homeomorphisms like H in the above theorem is called a local topological conjugacy between the (parametrized) flows defined by Fµ and F˜µ . Preliminaries of dynamical systems theory 33 Fig. 2. Hopf bifurcation in the positive case: dynamics for µ < 0, µ = 0, respectively µ > 0.

E. homeomorphisms. In this case we have indeed something like ‘local structural stability’ at hyperbolic stationary points. 1. This is the reason that we mainly consider C 0 conjugacies, also called topological conjugacies. As already mentioned before (see the discussion on the Hopf bifurcation), a conjugacy maps periodic evolutions to periodic evolutions with exactly the same period. In the case when the time set is R, the period can be any (positive) real number. Such a period can be changed by a perturbation which is arbitrarily small in the C k sense.

45 46 49 51 55 59 60 66 68 69 70 72 74 78 78 79 80 81 1 The first author was partially supported by NSF Grant No. DMS0616585.