Topologically conjugate

ThenWs(gfe( j) and Wu 7e(t)) intersect transversely at(xh(rio)+0(e),9 j and consequently (from, theS male-Birkhoff homoclinic theorem) for the map P there exists an integer n > 1 that P has an invariant Cantor set on which it is topologically conjugate to a full shift of N symbols. 

This result is due to Palis, who had fotmd that two-dimensional diffeomor-phisms with a heteroclinic orbit at whose points an unstable manifold of one saddle fixed point has a quadratic tangency with a stable manifold of another saddle fixed point can be topologically conjugated locally only if the values of some continuous invariants coincide. These continuous invariants are called moduli. Some other non-rough examples where moduli of topological conju-gacy arise are presented in Sec. 8.3. 

Theorem 13.13. If the set N of Theorem 13.11 is quasiminimal with a rotation number P, then the flow on N is topologically conjugate to a special Cherry flow restricted to its quasiminimal set) with a rotation number / . 

Roseophilin (273), a deeply red-colored pentacyclic compound isolated from the culture broth of Streptomyces griseoviridis, is a novel antitumor antibiotic. Compound 273 possesses a topologically unique pentacyclic skeleton, consisting of a 13-membered macrocycle incorporated in an ansa-bridged azafulvene, which in turn is linked to a conjugated heterocyclic ring system. The absolute stereochemistry of roseophilin, as depicted in Fig. 9, was unknown until the first total synthesis published by Tius and Harrington in 2001 [125]. All syn-... 

Fig. 12 The extension of some topological units into the more complex cychc jc-conjugated diradicals...

Porphyrin is a multi-detectable molecule, that is, a number of its properties are detectable by many physical methods. Not only the most popular nuclear magnetic resonance and light absorption and emission spectroscopic methods, but also the electron spin resonance method for paramagnetic metallopor-phyrins and Mossbauer spectroscopy for iron and tin porphyrins are frequently used to estimate the electronic structure of porphyrins. By using these multi-detectable properties of the porphyrins of CPOs, a novel physical phenomenon is expected to be found. In particular, the topology of the cyclic shape is an ideal one-dimensional state of the materials used in quantum physics [ 16]. The concept of aromaticity found in fuUerenes, spherical aromaticity, will be revised using TT-conjugated CPOs [17]. 

Lengthening the side chain produces the antidepressant maprotiline (73), which has a topological relationship to the clinically useful tricyclic antidepressants. The requisite acid is constructed by conjugate addition of the carbanion of anthrone (64) to acrylonitrile, followed by hydrolysis to give 70. Reduction of the carbonyl group with zinc and ammonia gives anthracene 71 by dehydration of the intermediate... 

The characteristic valence four of the C-atom is the origin of the enormous variety of these systems. Purely steric and topological considerations indicate that carbon conjugated polymeric structures can be either one- or two- dimensional since the conju-... 

A. Graovac, I. Gutman and N. Trinajstic, Topological Approach to the Chemistry of Conjugated Molecules, Springer-Verlag, Berlin, 1972. 

The enhanced stabilizations of benzene are apparently due to the unique cyclic conjugative topology in which all sites are of closed-CT type. Each site thereby participates in complementary bi-directional donor-acceptor interactions,... 

To achieve non-zero 7ta—7tb conjugation, the pi NBOs of 18 may polarize in opposite directions, leading to a wavefunction of lower symmetry than the nuclear framework. Alternatively, the nuclear framework may distort to diamond-like D2h geometry. However, each such distortion destabilizes what is already a highly unfavorable Lewis-structure wavefunction, so cyclobutadiene is expected to remain highly destabilized relative to other possible polyene topologies. 

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