Sullivan's Theory Research Articles

Patterson–Sullivan theory for groups with a strongly contracting element

Abstract Using Patterson–Sullivan measures, we investigate growth problems for groups acting on a metric space with a strongly contracting element.

Patterson–Sullivan theory for Anosov subgroups

We extend several notions and results from the classical Patterson–Sullivan theory to the setting of Anosov subgroups of higher rank semisimple Lie groups, working primarily with invariant Finsler metrics on associated symmetric spaces. In particular, we prove the equality between the Hausdorff dimensions of flag limit sets, computed with respect to a suitable Gromov (pre-)metric on the flag manifold, and the Finsler critical exponents of Anosov subgroups.

Professional Development and its Relationship with some Variables in the Light of Sullivan Theory among Male and Female Teachers in the Basic Education Schools in Sultanate of Oman

The study aims to reveal the level of professional development in basic education schools from the male and female teachers’ viewpoint in the Sultanate of Oman. It further aims to examine its relationship with some variables in light of Sullivan theory, and the differences in the level of professional development (teachers’ skills, professional participation, professional development problems) according to the gender variable, and the educational stage (first cycle/ second cycle). The study sample consisted of (93) teachers distributed as such: (46) male teachers, and (47) female teachers. A questionnaire was prepared and applied to measure the level of the professional development of the male and female teachers. The questionnaire consisted of (45) paragraphs. The researcher analyzed the means, standard deviations, and (T) test. Results have shown that that there is a high level of professional development among male and female teachers in the basic education schools in the Sultanate of Oman. Moreover, the dimensional levels have come first after teachers’ skills, second after professional participation, and third after professional development problems. Further, there are no statistically significant differences attributed to the gender and the educational stage variables (first cycle/ second cycle). The study has recommended the importance of benefiting from the applications of psychology and its theories in building, and developing the personalities of male and female teachers and in education sector’s professionals professionally, scientifically, socially, psychologically and academically. It has also recommended to encourage male and female teachers to pursue postgraduate studies and employ procedural research in electronic training and professional development operations.

Directions in orbits of geometrically finite hyperbolic subgroups

AbstractWe prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case with two recent infinite-volume exceptions by Zhang for Apollonian circle packings and certain Schottky groups. Our results hold for general Zariski dense, non-elementary, geometrically finite subgroups in any dimension. Unlike in the lattice case orbits of geometrically finite subgroups do not necessarily equidistribute on the whole boundary of hyperbolic space. But rather they may equidistribute on a fractal subset. Understanding the behavior of these orbits near the boundary is central to Patterson–Sullivan theory and much further work. Our theorem characterises the higher order spatial statistics and thus addresses a very natural question. As a motivating example our work applies to sphere packings (in any dimension) which are invariant under the action of such discrete subgroups. At the end of the paper we show how this statistical characterization can be used to prove convergence of moments and to write down the limiting formula for the two-point correlation function and nearest neighbor distribution. Moreover we establish a formula for the 2 dimensional limiting gap distribution (and cumulative gap distribution) which also applies in the lattice case.

Weighted cogrowth formula for free groups

We investigate the relationship between geometric, analytic and probabilistic indices for quotients of the Cayley graph of the free group {\rm Cay}(F_n) by an arbitrary subgroup G of F_n . Our main result, which generalizes Grigorchuk's cogrowth formula to variable edge lengths, provides a formula relating the bottom of the spectrum of weighted Laplacian on G \backslash {\rm Cay}(F_n) to the Poincaré exponent of G . Our main tool is the Patterson–Sullivan theory for Cayley graphs with variable edge lengths.

Manhattan curves for hyperbolic surfaces with cusps

In this paper, we study an interesting curve, the so-called Manhattan curve, associated with a pair of boundary-preserving Fuchsian representations of a (non-compact) surface; in particular, representations corresponding to Riemann surfaces with cusps. Using thermodynamic formalism (for countable state Markov shifts), we prove the analyticity of the Manhattan curve. Moreover, we derive several dynamical and geometric rigidity results, which generalize results of Burger [Intersection, the Manhattan curve, and Patterson–Sullivan theory in rank 2. Int. Math. Res. Not.1993(7) (1993), 217–225] and Sharp [The Manhattan curve and the correlation of length spectra on hyperbolic surfaces. Math. Z.228(4) (1998), 745–750] for convex cocompact Fuchsian representations.

Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions

In this paper, we use Chas–Sullivan theory on loop homology and Leray–Serre spectral sequence to investigate the topological structure of the non-contractible component of the free loop space on the real projective spaces with odd dimensions. Then we apply the result to get the resonance identity of non-contractible homologically visible prime closed geodesics on such spaces provided the total number of distinct prime closed geodesics is finite.

Cheeger constants and L2-Betti numbers

We prove the existence of positive lower bounds on the Cheeger constants of manifolds of the form X/Γ where X is a contractible Riemannian manifold and Γ<Isom(X) is a discrete subgroup, typically with infinite covolume. The existence depends on the L2-Betti numbers of Γ, its subgroups, and a uniform lattice of Isom(X). As an application, we show the existence of a uniform positive lower bound on the Cheeger constant of any manifold of the form H4/Γ where H4 is real hyperbolic 4-space and Γ<Isom(H4) is discrete and isomorphic to a subgroup of the fundamental group of a complete finite-volume hyperbolic 3-manifold. Via Patterson–Sullivan theory, this implies the existence of a uniform positive upper bound on the Hausdorff dimension of the conical limit set of such a Γ when Γ is geometrically finite. Another application shows the existence of a uniform positive lower bound on the zeroth eigenvalue of the Laplacian of Hn/Γ over all discrete free groups Γ<Isom(Hn) whenever n≥4 is even. (The bound depends on n.) This extends results of Phillips–Sarnak and Doyle, who obtained such bounds for n≥3 when Γ is a finitely generated Schottky group.

A smooth variation of Baas–Sullivan theory and positive scalar curvature

Let \(M\) be a smooth closed spin (resp. oriented and totally non-spin) manifold of dimension \(n\ge 5\) with fundamental group \(\pi \). It is stated, e.g. by Rosenberg and Stolz (Surv Surg Theory 2, pp. 353–370, 2001), that \(M\) admits a metric of positive scalar curvature (pscm) if its orientation class in \(ko_n(B\pi )\) (resp. \(H_n(B\pi ;\mathbb Z )\)) lies in the subgroup consisting of elements which contain pscm representatives. This is \(2\)-locally verified loc. cit. and by Stolz (Topology 33, pp. 159–180, 1994). After inverting \(2\) it was announced that a proof would be carried out by Jung (uncompleted Ph.D. thesis), but this work has never appeared in print. The purpose of our paper is to present a self-contained proof of the statement with \(2\) inverted.

A Cr unimodal map with an arbitrary fast growth of the number of periodic points

AbstractIn this paper we present a surprising example of a Cr unimodal map of an interval f:I→I whose number of periodic points Pn(f)=∣{x∈I:fnx=x}∣ grows faster than any ahead given sequence along a subsequence nk=3k. This example also shows that ‘non-flatness’ of critical points is necessary for the Martens–de Melo–van Strien theorem [M. Martens, W. de Melo and S. van Strien. Julia–Fatou–Sullivan theory for real one-dimensional dynamics. Acta Math.168(3–4) (1992), 273–318] to hold.

“That's Just Who I Am”: How the Ambiguities of Language Influence Our Concept of Personality and Negatively Impact Couple Relationships

Informed by the insights of the philosopher Ludwig Wittgenstein, this article aims to uncover how the ambiguities of language engender misleading but commonly held assumptions and beliefs about personality as a fixed and unchanging entity that contribute to significant problems in couple relationships. Henry Stack Sullivan's interpersonal theory is used to provide a framework for an alternative understanding of personality as a malleable entity that is rooted in experience and shaped by learned behavior, with the further implication that personality therefore is subject to change through new experience and newly developed patterns of behavior. A clinical example provides an illustration of how a couple can become ensnared into an impasse in their relationship because of how the ambiguities of language lead them to assume that personality is fixed and unchanging, and how the clinician, informed by Sullivan's theory of personality, can help the couple break free from the impasse so that they are enabled to be more responsive to one another's concerns through a process of reciprocal change. Implications from this analysis are drawn relative to Andrew Christensen and Neil Jacobson's acceptance theory of change as well as John Gottman's theory about perpetual problems.

Louis H. Sullivan and a 19th-century poetics of naturalized architecture

Contents: Preface Introduction: reviewing Sullivan after modernism The romantic context and Emerson's poetic project for an American art John Ruskin: the picturesque discourse and the language of architectural naturalism Gothic naturalism and the Ruskinian critical tradition in America The auditorium building: a Ruskinian reading Ruskin's reception in the Chicago school Sullivan's emergence as a landscape poet-architect Naturalized technology: Sullivan's theory of skyscraper design Ut pictura architectura: Sullivan's pictorial techniques for representing nature in architecture The transportation building: Sullivan's manifesto of poeticized architecture Epilogue: the problem of Sullivan's poetic legacy Selected bibliography Index.

Applying Sullivan's Theory of Anxiety versus Fear

Applying Sullivan's Theory of Anxiety versus FearClarence G. SchulzClarence G. Schulz1. Washington Psychoana-lytic Institute; Clinical Professor of Psychiatry, University of Maryland School of Medicine; Assistant Pro-fessor of Psychiatry, Johns Hopkins MedicineSearch for more papers by this authorPublished Online:July 2006https://doi.org/10.1521/psyc.2006.69.2.110PDFPDF PLUS ShareShare onFacebookTwitterLinkedInRedditEmail ToolsAdd to favoritesDownload CitationsTrack Citations AboutReferencesMoreno, J. (1934). Who shall survive? Washington, DC: Nervous and Mental Disease Publishing Co. Google ScholarMoreno, J. (1969). Psychodrama (Vol. 3). Beacon, NY: Beacon House. Google ScholarMullahy , P. (1947). A theory of interpersonal relations and the evolution of personality. In H. Sullivan (Ed.), Conceptions of modern psychiatry. Washington, D.C.: William Alanson White Foundation. Google ScholarSchulz , C. (1978). Sullivan's clinical contribution during the Sheppard Pratt Era: 1923–1930. Psychiatry, 41, 117–128. Crossref Medline, Google ScholarStanton , A., & Schwartz, M. (1954). The mental hospital. New York: Basic Books. Google ScholarSullivan , H. (1949). The theory of anxiety and the nature of psychotherapy. Psychiatry, 12, 3–12. Crossref Medline, Google ScholarWhite , M. (1977). Sullivan and treatment. Journal of Contemporary Psychoanalysis, 13, 317–346. Crossref, Google Scholar Previous article Next article FiguresReferencesRelatedDetails Cited byCited by1. The Feeling of Fear among Local Government Administration Employees as a Result of the Introduction of E-AdministrationOnline publication date: 4 September 2020. Go to citation Crossref Google Scholar Volume 69Issue 2Mar 2006 Information© Guilford Publications Inc.PDF download

Same-Sex Peer Relations and Romantic Relationships During Early Adolescence: Interactive Links to Emotional, Behavioral, and Academic Adjustment

It was examined whether early adolescents' involvement in a romantic relationship would be differentially related to adjustment, depending on their relations with the same-sex peer group. Three hundred and twelve 7th graders were assessed with respect to their social acceptance by same-sex peers, involvement in reciprocal same-sex friendships, involvement in romantic relationships, self-esteem, antisocial behavior, and academic performance. Social acceptance by other-sex peers and involvement in reciprocal other-sex friendships were also assessed for control purposes. The results showed that having a boyfriend/ girlfriend was related to poorer emotional and behavioral adjustment for those early adolescents who were unpopular among same-sex peers. For adolescents who were popular among same-sex peers, romantic involvement was not related to emotional and behavioral adjustment. Independently of same-sex peer acceptance, however, romantic involvement was negatively related to academic performance, albeit only for girls. The results are discussed in light of Sullivan's theory of social development.

The Use of Communication to Motivate College Sales Teams

This study explored how sales managers and sales people construct and perform motivational communication. Sullivan's (1988) Motivational Language Theory (MLT) was used as a starting point. This the...

Freud's theory of paranoid delusion based on the Schreber case contrasted with related theories

The historic importance of Freud's analysis of the Schreber case is acknowledged, even though the theory it expounds is largely disavowed. The theory ascribes the cause of paranoid delusion to homosexual impulses unresolved in infancy or early childhood. This paper summarizes Freud's monograph on Schreber and contrasts his theory with the views of various revisionists. The writers focus on the Freudian concept of projection, which is intended to explain how much meaning can become reversed under the impetus of stress, and the reversal lead to delusional thinking. Based on their work in family therapy, where they observed one form of pathogenic relating termed learning to be possessed, the writers concluded that this form was also based on a type of projection which could culminate in delusional ideation. A relationship between learning to be possessed and H. S. Sullivan's theory of paranoid transformation is described. A learning factor is present in several of the psychological theories advanced to explain delusion, and the factor is akin to if not identical with Freud's concept of projection.

Adolescents from Divorced Families and Their Best-Friend Relationships

The present study examines the quality of best-friend relationships of adolescent children of divorced parents. Two theoretical frameworks are employed: Sullivan's substitution theory, and Freud's object-relation theory. The findings of the study show that parental divorce (1) has no effect on either having a best-friend relationship or satisfaction with social life; (2) has only a slight effect on the perception of the best-friend relationship; (3) has a somewhat greater effect on the experience of the best-friend relationship. These results are interpreted and shown to lend some support to the object relation theory.

Albert J. Sullivan's theory of public relations ethics

Albert J. Sullivan's theory of public relations ethics

Assessing the cognitive-interpersonal cycle

This article argues that Harry Stack Sullivan's conceptions of interpersonal psychotherapy have a number of important implications for both the theory and practice of cognitive behavior therapy. Sullivan's formulations, while compatible with cognitive behavioral theory in many respects, add both motivational and interpersonal contexts that are missing from cognitive behavior therapy. With regard to the first theme, it is argued that Sullivan's theory on the role of anxiety in the development and maintenance of dysfunctional cognitive structures has important implications for both cognitive assessment and modification. With regard to the second theme, it is argued that the therapist's role as a participant-observer in the therapeutic relationship provides him with a valuable opportunity for identifying maladaptive interpersonal patterns and assessing dysfunctional cognitive activities that are linked to these patterns.

Bureaucracy as Externalized Self-System

In this article the author uses Harry Stack Sullivan's theory of social psychiatry and various psychoanalytic applications of organizational theory to suggest to what extent bureaucratized human relations and formal organizational stuctures are products of the psyche and thereby perpetuated by people. A central theme is that bureaucracy enhances the structural manifestation of embedded defensive operations of the person. Asserting the dominance of security needs as motivating forces over other human needs, Sullivan's psychiatry uncovers a serious paradox for students of organizational behavior and development interested in directing the course of bureaucratic reform and organizational change. This article directs future empirical research on the topic of interpersonal and organizational resistance to change and psychological reliance on bureaucratic styles of management.