We recall the notion of Jacobi fields, as it was extended to systems of second-order ordinary differential equations. Two points along a base integral curve are conjugate if there exists a non-trivial Jacobi field along that curve that vanishes on both points. Based on arguments that involve the eigendistributions of the Jacobi endomorphism, we discuss conjugate points for a certain generalization (to the current setting) of locally symmetric spaces. Next, we study conjugate points along relative equilibria of Lagrangian systems with a symmetry Lie group. We end the paper with some examples and applications.
We investigate Jacobi fields and conjugate points in the context of sprays. We first prove that the conjugate points of a spray remain preserved under a projective change. Then, we establish conditions on the projective factor so that the projectively deformed spray meets the conditions of a proposition that ensures the existence of conjugate points. We discuss our methods by means of illustrative examples, throughout the paper.
1956: desire and the unknowable is my first response to my father's photographs of the Hungarian Uprising of October 1956. The paper emerges from my position as a member of the Hungarian diaspora, whereby my very existence and identity as a member of a diaspora owes itself to a historical event that I am unable to lay claim to. The work traces tensions created by multiple desires - in diasporic longing, in positivist history-making, and in the demands put on the photograph as unmediated historical evidence. This paper is an adaptation from a chapter in my Masters dissertation - Little Histories. It opens with an outline of the context of production of the original images, as well my responses to these images. It then goes on to discuss issues that have had a significant impact on the creation of the work, whether arising from the original images or from critical theory. The overriding notion is that vernacular photographs can be used to contest and replace images and ideologies that have come to dominate our memories of the past, and that the past becomes meaningful through such acts of engagement. 1956: desire and the unknowable was first exhibited in a solo exhibition, Little Histories, at the Sydney College of the Arts in 2001. Later that year it was presented, together with 30 of my father’s original photographs, in a father-daughter collaborative exhibition at 62 Robertson, Brisbane. Between Ranke and the sublime: two approaches to Budapest 1956 presented opposing modernist and post-modern views about the ability of the photograph to provide knowledge of the past. The work was most recently shown again at a residency in CESTA, in the Czech Republic, as part of a site-specific installation. In the country where my father once walked I presented a selection of my father’s work at the Szabo Ervin Library, Budapest, in 2001.
Encountering Saigon in the early 1990s, I was confronted with an unfamiliar concept of time in photography. I am not talking about moments, the tripping of shutters, the splattering of light onto a frame of film. No, I am referring to historical time. Time as epochs. Time that lingered thick and dense like heavy wedges or chunks that could barely be budged.
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