Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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Introduction to the Modern Theory of Dynamical Systems

Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the orbits and introduction to ergodic theory 5. Smooth invariant measures and more examples Part II. Local Analysis and Orbit Growth 6. Local hyperbolic theory and its applications 7. Transversality and genericity 8. Orbit growth arising from topology 9. Variational aspects of dynamics Part III. Low-Dimensional Phenomena 10. Introduction: What is low dimensional dynamics 11. Homeomorphisms of the circle 12. Circle diffeomorphisms 13. Twist maps 14. Flows on surfaces and related dynamical systems 15. Continuous maps of the interval 16. Smooth maps of the interval Part IV. Hyperbolic Dynamical Systems 17. Survey of examples 18. Topological properties of hyperbolic sets 19. Metric structure of hyperbolic sets 20. Equilibrium states and smooth invariant measures Part V. Sopplement and Appendix 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.

Introduction to the Modern Theory of Dynamical Systems: EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES

Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION: WHAT IS LOW-DIMENSIONAL DYNAMICS?

Normal forms and desingularization Singular points of planar analytic vector fields Local and global theory of linear systems Functional moduli of analytic classification of resonant germs and their applications Global properties of complex polynomial foliations Appendix. First aid Bibliography Index.

/pdf/lectures-on-analytic-differential-equations-1b5sepa58b.pdf

Lectures on analytic differential equations

Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class (i.e. between C1 and C2). In particular, we show some generalizations of Denjoy theorem and the classical Kopell lemma for abelian groups. These techniques are also applied to the study of codimension-1 foliations. For instance, we obtain several generalized versions of Sacksteder theorem in class C1. We conclude with some remarks about the stationary measure.

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Sur la dynamique unidimensionnelle en régularité intermédiaire

Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class ({\em i.e.} between $C^1$ and $C^2$). In particular, we demonstrate some generalizations of Denjoy's Theorem and the classical Kopell's Lemma for Abelian groups. After that, these techniques are applied to the study of codimension 1 foliations. We obtain for instance several generalized versions of Sacksteder's Theorem in class $C^1$. We conclude with some remarks about the stationary measure.

Sur la dynamique unidimensionnelle en r\'egularit\'e interm\'ediaire

Aggregation of individual wavelengths into wavebands for their subsequent switching and routing as a single group is an attractive way for scalable and cost-efficient optical networks. We analyze the implications of this waveband hierarchy for a single optical node by analyzing two issues: the proper selection of waveband sizes and the assignment of wavebands for a limited set of input-output patterns of traffic. We formulate a general model and propose optimal algorithmic solutions for both problems. The performance of resulting sets of nonuniform wavebands is studied for several representative cases (a single node, an optical ring network, an optical mesh network). The results demonstrate improved optical throughput and reduced cost of switching and routing when using nonuniform waveband hierarchy.

/pdf/nonuniform-waveband-hierarchy-in-hybrid-optical-networks-30qjm0vmca.pdf

Nonuniform waveband hierarchy in hybrid optical networks

We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversally conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove that either there exists a measure invariant under all the elements of the group (or the pseudo-group), or almost surely a long composition of maps contracts a ball exponentially. We deduce some results about the unique ergodicity.

Random Conformal Dynamical Systems

This work is devoted to the study of minimal, smooth actions of finitely generated groups on the circle. We provide a sufficient condition for such an action to be ergodic (with respect to the Lebesgue measure), and we illustrate this condition by studying two relevant examples. Under an analogous hypothesis, we also deal with the problem of the zero Lebesgue measure for exceptional minimal sets. This hypothesis leads to many other interesting conclusions, mainly concerning the stationary and conformal measures. Moreover, several questions are left open. The methods work as well for codimension-one foliations, though the results for this case are not explicitly stated.

Victor Kleptsyn

Papers

Sur la dynamique unidimensionnelle en régularité intermédiaire

Sur la dynamique unidimensionnelle en r\'egularit\'e interm\'ediaire

Nonuniform waveband hierarchy in hybrid optical networks

Random Conformal Dynamical Systems

On the question of ergodicity for minimal group actions on the circle