Aziridine-Metathesis based Approaches to Alkaloid Synthesis

The aim of the project is to synthesise (-)-morphine utilising aziridine and metathesischemistry. The thesis is divided into three chapters.Chapter 1 provides brief reviews on the subjects of total synthesis of morphine; ringrearrangementmetathesis (RRM) and regioselective ring-opening of aziridines.Chapter 2 focuses on the research findings in the past three years. Two routes, A and B,were investigated in attempts to synthesise morphine (Scheme 1). In route A, sulfonylcyclopentene II was prepared from ring-closing metathesis of a diene precursor, whichwas synthesised from lithiated cinnamylsulfone and butadiene monoxide. Subsequently,RRM reactions of several [alpha]-SO2Ph allyl derivatives of II were investigated and someinteresting results were obtained. The synthesis of 2,3-trans vinylaziridine III wasachieved in seven steps beginning with a Grignard reaction of (4-methoxyphenyl)magnesium bromide with butadiene monoxide. Subsequently, somehighly regioselective ring-opening reactions of III with sulfur-stabilised anionicnucleophiles were achieved. However, in an attempt to synthesise compound I from IIand III, no reaction was observed. This led to the investigation of route B, in which fivemethods for the synthesis of compound IV were investigated. The practical approachdeployed a novel Al-mediated substitution of the 4-tosyl group of the tosyltetrahydropyridine counterpart of IV, prepared from V and III, with a phenylthio group.Chapter 3 provides the experimental details and characterisation data.Imperial Users onl

Homoclinic intersections of symplectic partially hyperbolic systems with 2D center

We study some generic properties of partially hyperbolic symplectic systems with 2D center. We prove that $C^r$ generically, every hyperbolic periodic point has a transverse homoclinic intersection for the maps close to a direct/skew product of an Anosov diffeomorphism with a map on $S^2$ or $\mathbb{T}^2$

Partially hyperbolic sets with positive measure and ACIPACIP for partially hyperbolic systems

In [Discrete Contin. Dyn. Syst. \textbf{15} (2006), no. 3, 811--818.] Xia introduced a simple dynamical density basis for partially hyperbolic sets of volume preserving diffeomorphisms. We apply the density basis to the study of the topological structure of partially hyperbolic sets. We show that if $\Lambda$ is a strongly partially hyperbolic set with positive volume, then $\Lambda$ contains the global stable manifolds over ${\alpha}(\Lambda^d)$ and the global unstable manifolds over ${\omega}(\Lambda^d)$. We give several applications of the dynamical density to partially hyperbolic maps that preserve some $acip$. We show that if $f$ is essentially accessible and $\mu$ is an $acip$ of $f$, then $\text{supp}(\mu)=M$, the map $f$ is transitive, and $\mu$-a.e. $x\in M$ has a dense orbit in $M$. Moreover if $f$ is accessible and center bunched, then either $f$ preserves a smooth measure or there is no $acip$ of $f$.Comment: Correct the proof of Theorem 5.5. Add a few explanation

A diffeomorphism with global dominated splitting can not be minimal

Let M be a closed manifold and f be a diffeomorphism on M. We show that if f has a nontrivial dominated splitting TM=E\oplus F, then f can not be minimal. The proof mainly use Mane's argument and Liao's selecting lemma.Comment: 5 pages. An application of Liao's selecting lemm