22,816 research outputs found
Addendum: an analogue of Artin reciprocity for closed orbits of skew products
No full textOne of the unfulfilled aims of the authors of the preceding paper [W. Parry and M. Pollicott. An analogue of Bauer’s theorem for closed orbits of skew products. Ergod. Th. & Dynam. Sys. 28 (2008), 535–546] was to find a dynamical analogue of Artin reciprocity. In this addendum, we present one such version, suggested by work of Sunada
Controlling the statistical properties of expanding maps
No full textHow can one change a system, in order to change its statistical properties in a prescribed way? In this note we consider a control problem related to the theory of linear response. Given an expanding map of the unit circle with an associated invariant density we can consider the inverse problem of finding which first order changes in the transformation can achieve a given first order perturbation in the density. We show the general mathematical structure of the problem, the existence of many solutions in the case of expanding maps of the circle and the existence of optimal ones. We investigate in depth the example of the doubling map, where we give a complete solution of the problem
ASYMPTOTIC VERTEX GROWTH FOR GRAPHS Mark Pollicott
No full textIntroduction In this note, we want to describe a useful invariant for weighted graphs and characterize the minima of this quantity over all weightings which are suitably normalized. In the case of regular graphs this minima occurs precisely at the unweighted graphs, i.e., where the weighting for each of the edges is taken to be 1. Thus, the regular graphs are characterized as being extremal for this invariant. (cf. the paper of Jakobson and Rivin [4] where other invariants with the property are studied). An unweighted graph = (V, E) consists of a finite set of vertices and edges E . If we assume for convenience that there is at most one edge e joining a pair of vertices (i, j) # V V then we can identify E # V V. Since we are interested in undirected graphs we assume that (i, j) if and only if (j, i) . Let denote the number of edges and denote the number of vertices. Ordinarily, we would think of as having edges of unit length. However, additional structure can
Effective estimates of Lyapunov exponents for random products of positive matrices
No full textIn this note we describe estimates on the error when calculating the Lyaponov exponent for random products of positive matrices using dynamical determinants. This extends the results in (Jurga N and Morris I 2019 Nonlinearity 32 4117–46; Pollicott M 2010 Invent. Math. 181 209–26) by drawing upon a new approach introduced in (Jenkinson O and Pollicott M 2018 Adv. Math. 325 87–115; Jenkinson O, Pollicott M and Vytnova P 2018 J. Stat. Phys. 170 221–53)
The sense of a beginning : Bakhtinian dialogic criticism on 'the gospel' in Mark.
No full textContemporary literary approaches have caused paradigm shifts in Biblical Studies in the last two decades as it appears in a great deal of Markan studies using narrative, reader-response, deconstructive, feminist, and new historicist approaches. However, literary studies on the Gospel of Mark have not taken into account theoretical questions underlying those approaches. As a result biblical critics are driven by new trends without ever having a chance to examine the critical baggage of the approaches. Consequently, there is a gap of communication between the old and the new one. Therefore this thesis is an attempt to meet the need of enhancing the quality of critical endeavour in biblical studies. In the light of most recent competing critical theories of literature, the first contribution of this thesis is the methodological finding that Bakhtinian dialogic criticism contains the most profound philosophical and practical foundations for solving some crucial theoretical problems in contemporary literary theories. It is a critique to a Saussurian linguistic system of language which becomes the very foundation of modern and postmodern literary criticism. Bakhtinian literary theory shifts the foundation of literary criticism on linguistic signs into the creative activity of the socio-cultural production of human communication. The shift into socio-cultural reality of language communication makes the notion of 'genre' very important to unlock the problem of text and context in literary studies. Since the Gospel of Mark has fascinated most literary critics in Biblical Studies, the problem of 'genre' of this gospel is chosen as the focus of this study. Secondly, as no agreement is reached as to what 'genre' the Gospel of Mark belongs, this thesis makes its contribution to the discussion by locating the problem of 'genre' of Mark in the context of genre theories and argues that the Bakhtinian suggestion to find genre in the socio-cultural sphere by analysing artistic intercourse between narrative agents in Mark has freed the competing analysis from the unresolved problem between the kerygmatic (content oriented) approach and the analogical (form oriented) approach. To achieve finding 'genre' in the socio-cultural sphere, this thesis focuses on Bakhtinian analysis of the process of artistic intercourse between narrative agents. The narrative communicative interrelationships between narrative agents is constructed in this thesis as a 'stereophonic' Bakhtinian model of dialogic communication. This model is an original contribution of this thesis for revising the traditional two dimensional model of narrative communication. Based on this dialogical model of communication, a special role is given to the Bakhtinian 'author-creator' in the realization process of genre through the interaction of polyphonic voices. Through the interaction of voices of the author-artist and the hero we are led to discover a relatively stable type of portraying and controlling reality in Mark, known as the genre of Roman 'satire'. The closest literary affinity is Satyrica by Petronius. This narrative strategy of 'satire' in Mark has its root in the prophetic discourse of the Old Testament which is saturating the speech of the narrator, John the Immerser, the centurion, the people, and even Jesus. Finally, the whole search for Markan 'genre' culminates in the analysis of the realization of genre through the analysis of Bakhtinian chronotope. The reality of the genre of Mark is its social reality that is in its role as dpxrj/ 'beginning'. As the Gospel of Mark proclaims itself as 'a beginning', it defines its claim of socio-cultural 'authority' in early Christianity. It is this 'sense of beginning' which enables the narrating and the narrated world of Mark to interact dialogically
Anosov flows and dynamical Zeta functions
No full textWe study the Ruelle and Selberg zeta functions for Cr Anosov flows, r>2, on a compact smooth manifold. We prove several results, the most remarkable being: (a) for C∞ flows the zeta function is meromorphic on the entire complex plane; (b) for contact flows satisfying a bunching condition (e.g. geodesic flows on manifolds of negative curvature better than 19-pinched) the zeta function has a pole at the topological entropy and is analytic in a strip to its left; (c) under the same hypotheses as in (b) we obtain sharp results on the number of periodic orbits. Our arguments are based on the study of the spectral properties of a transfer operator acting on suitable Banach spaces of anisotropic currents
Democracy Sausage with Mark Kenny: How to be a liberal with Ian Dunt
No full textOn this Democracy Sausage Extra, Ian Dunt - host of the Oh God, What Now? podcast and author of How to be a liberal - joins Mark Kenny to discuss the history of liberal thought, how it has shaped present day politics, and the origins of the ‘culture wars’. Have the culture wars emerged out of the failures of liberalism? Why haven’t contemporary political actors done more to protect people from prejudice and the tyranny of the majority? And is liberalism a natural corollary to democracy? On this Democracy Sausage Extra, author, political journalist and broadcaster Ian Dunt joins Professor Mark Kenny to discuss the history of political thought, present day politics, and liberalism’s trajectory
[Interview with Mark Lane in Playboy Magazine #3]
No full textPoor quality photocopies of a magazine article which appeared in Playboy Magazine. The article features an extensive interview with Mark Lane, an attorney and author, who is critical of the Warren Commission's assessment of the assassination of President Kennedy
Democracy Sausage with Mark Kenny: Full circle with Scott Ludlam
No full textOn this episode of Democracy Sausage, Scott Ludlam, former Greens Deputy Leader and author of the new book Full Circle: A search for the world that comes next, joins Mark Kenny to discuss what he learnt from his time in politics and Australian climate policy. What role do corporate and private interests play in shaping Australian policy-making? Will the country make changes to political donation rules to make the system more transparent? And how can Australia make meaningful progress on climate policy? On this episode of Democracy Sausage, Professor Mark Kenny speaks with former Greens Senator Scott Ludlam about Australian politics, his new book, and Section 44 of the Constitution
- …
