Self-similarity in the Kepler-Heisenberg problem\nby Corey Shanbro m (CSUS) as part of Sydney Dynamics Group Seminar\n\n\nAbstract\nThe Keple r-Heisenberg problem is that of determining the motion of a planet around a sun in the Heisenberg group\, thought of as a three-dimensional sub-Riem annian manifold. The sub-Riemannian Hamiltonian provides the kinetic energ y\, and the gravitational potential is given by the fundamental solution t o the sub-Laplacian. The dynamics are at least partially integrable\, poss essing two first integrals as well as a dilational momentum which is conse rved by orbits with zero energy. The system is known to admit closed orbit s of any rational rotation number\, which all lie within the fundamental z ero energy integrable subsystem. Here\, we demonstrate that all zero energ y orbits are self-similar.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Mariusz Urbanski (UNT) DTSTART;VALUE=DATE-TIME:20201105T230000Z DTEND;VALUE=DATE-TIME:20201106T000000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/13 DESCRIPTION:Title: Random non-hyperbolic exponential maps\nby Mariusz Urbanski (UNT) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SDGSeminar/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandro Vaienti (Toulon) DTSTART;VALUE=DATE-TIME:20201028T070000Z DTEND;VALUE=DATE-TIME:20201028T080000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/14 DESCRIPTION:Title: On some recent applications of extreme value theory to dynamical syste ms\nby Sandro Vaienti (Toulon) as part of Sydney Dynamics Group Semina r\n\n\nAbstract\nWe review a few applications of extreme value theory to: \n \n(i) open systems\; \n \n(ii) give the distribution of observables def ined along the temporal evolution of a\ndynamical system. \n \nApplicatio ns are given for the class of prevalent observables.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Montgomery (UC Santa Cruz) DTSTART;VALUE=DATE-TIME:20210312T030000Z DTEND;VALUE=DATE-TIME:20210312T040000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/15 DESCRIPTION:Title: Some open questions in the N-body problem\nby Richard Montgomery ( UC Santa Cruz) as part of Sydney Dynamics Group Seminar\n\n\nAbstract\nThe classical N-body problem\, despite being 333 years old\, is alive and wel l.\nI will begin with a pictorial survey of a few solution curves. I then state ``the\nproblem’’ and describe between two and four open questio ns within the problem and survey of recent progress on them.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Duignan (University of Colorado Boulder) DTSTART;VALUE=DATE-TIME:20210326T050000Z DTEND;VALUE=DATE-TIME:20210326T060000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/16 DESCRIPTION:Title: Integrability\, Normal Forms\, and Magnetic Axis Coordinates\nby N athan Duignan (University of Colorado Boulder) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SDGSeminar/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Atnip (University of New South Wales) DTSTART;VALUE=DATE-TIME:20210423T053000Z DTEND;VALUE=DATE-TIME:20210423T063000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/17 DESCRIPTION:Title: Random Interval Maps with Holes\nby Jason Atnip (University of New South Wales) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SDGSeminar/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Hester (University of Sydney) DTSTART;VALUE=DATE-TIME:20210430T060000Z DTEND;VALUE=DATE-TIME:20210430T070000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/18 DESCRIPTION:Title: Modelling fluid-solid interactions\nby Eric Hester (University of Sydney) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SDGSeminar/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Florica Cîrstea (University of Sydney) DTSTART;VALUE=DATE-TIME:20210513T060000Z DTEND;VALUE=DATE-TIME:20210513T070000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/19 DESCRIPTION:Title: Existence of singular solutions to elliptic equations with critical Ha rdy--Sobolev growth\nby Florica Cîrstea (University of Sydney) as par t of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SDGSeminar/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Cecilia Gonzáles-Tokman (University of Queensland) DTSTART;VALUE=DATE-TIME:20210528T060000Z DTEND;VALUE=DATE-TIME:20210528T070000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/20 DESCRIPTION:Title: Lyapunov exponents for transfer operator cocycles of random interval m aps\nby Cecilia Gonzáles-Tokman (University of Queensland) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SDGSeminar/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Monique Chyba (University of Hawaii) DTSTART;VALUE=DATE-TIME:20210610T230000Z DTEND;VALUE=DATE-TIME:20210611T000000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/21 DESCRIPTION:Title: Epidemiological modeling\, and COVID-19 Heterogeneity in Islands Chain Environment\nby Monique Chyba (University of Hawaii) as part of Sydne y Dynamics Group Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SDGSeminar/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Connor Jackman (CIMAT) DTSTART;VALUE=DATE-TIME:20210625T060000Z DTEND;VALUE=DATE-TIME:20210625T070000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/22 DESCRIPTION:Title: The geometry of (planar) Kepler orbits\nby Connor Jackman (CIMAT) as part of Sydney Dynamics Group Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SDGSeminar/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Wang (University of Sydney) DTSTART;VALUE=DATE-TIME:20210813T060000Z DTEND;VALUE=DATE-TIME:20210813T070000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/23 DESCRIPTION:Title: When random initialisations help: a study of variational inference for community detection\nby Rachel Wang (University of Sydney) as part of Sydney Dynamics Group Seminar\n\n\nAbstract\nVariational approximation ha s been widely used in large-scale Bayesian inference recently\, the simple st kind of which involves imposing a mean field assumption to approximate complicated latent structures. Despite the computational scalability of m ean field\, theoretical studies of its loss function surface and the conve rgence behaviour of iterative updates for optimising the loss are far from complete. In this paper\, we focus on the problem of community detection for a simple two-class Stochastic Blockmodel (SBM) with equal class sizes . Using batch co-ordinate ascent (BCAVI) for updates\, we show different convergence behaviour with respect to different initialisations. When the parameters are known or estimated within a reasonable range and held fixe d\, we characterise conditions under which an initialisation can converge to\nthe ground truth. On the other hand\, when the parameters need to be estimated iteratively\, a random initialisation will converge to an uninfo rmative local optimum.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Hinke Osinga (University of Auckland) DTSTART;VALUE=DATE-TIME:20210827T050000Z DTEND;VALUE=DATE-TIME:20210827T060000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/24 DESCRIPTION:Title: Computing periodic travelling waves and their stability in a heterocli nic-cycle model\nby Hinke Osinga (University of Auckland) as part of S ydney Dynamics Group Seminar\n\n\nAbstract\nHeteroclinic-cycle models are often used in ecology to describe cyclic dominant behaviour between compet ing populations. This so-called intransitive\, or non-hierarchical competi tion is thought to increase biodiversity\, because there is no single ‘b est’ competitor. We consider such models in the form of reaction-diffusi on PDEs\, which exhibit travelling waves in one spatial dimension and spir al waves in two spatial dimensions. The model also has travelling fronts f ormed by heteroclinic connections between two equilibria in a moving frame of reference\; these fronts are unstable\, but we find that large-wavelen gth traveling waves made up of three of these unstable travellings fronts can be stable. This talk includes a software demonstration of how to compu te the essential spectrum (and hence\, stability) of these large-wavelengt h travelling waves with the software package AUTO. Our computational appro ach for determining the stability boundary is based on the continuation sc heme developed by Rademacher\, Sandstede and Scheel (Physica D 229: 166– 83\, 2007). We highlight the enhancements implemented in our version\, inc luding the new idea of computing what we call `belts of instability'\, whi ch are indicators of the growth rate of unstable travelling waves. Our res ults from the stability analysis are verified by direct simulation and we also show how the computed growth rates accurately quantify the instabilit ies of the travelling waves.\n\nThis is joint work with Cris Hasan (UCCork ) Alastair Rucklidge (Leeds) and Claire Postlethwaite (University of Auckl and).\n LOCATION:https://researchseminars.org/talk/SDGSeminar/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Alfonso Sorrentino (University of Rome "Tor Vergata") DTSTART;VALUE=DATE-TIME:20210910T063000Z DTEND;VALUE=DATE-TIME:20210910T073000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/25 DESCRIPTION:Title: The Hamilton–Jacobi equation on networks: weak KAM and Aubry–Mathe r theories\nby Alfonso Sorrentino (University of Rome "Tor Vergata") a s part of Sydney Dynamics Group Seminar\n\n\nAbstract\nOver the last years there has been an increasing interest in the study of the Hamilton–Jaco bi Equation on networks and related questions. These problems\, in fact\, involve a number of subtle theoretical issues and have a great impact in t he applications in various fields\, for example to data transmission\, tra ffic management problems\, etc… While locally — i.e.\, on each branch of the network (arcs) —\, the study reduces to the analysis of 1-dimensi onal problems\, the main difficulties arise in matching together the infor mation converging at the juncture of two or more arcs\, and relating the l ocal analysis at a juncture with the global structure/topology of the netw ork.\nIn this talk I shall discuss several results related to the global a nalysis of this problem\, obtained in collaboration with Antonio Siconolfi (Univ. of Rome La Sapienza)\; more specifically\, we developed analogues of the so-called Weak KAM theory and Aubry–Mather theory in this setting . The salient point of our approach is to associate to the network an abst ract graph\, encoding all of the information on the complexity of the netw ork\, and to relate the differential equation to a discrete functional equ ation on the graph.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Chunxi Jiao (University of Sydney) DTSTART;VALUE=DATE-TIME:20210924T060000Z DTEND;VALUE=DATE-TIME:20210924T070000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/26 DESCRIPTION:Title: Solution of a stochastic Landau-Lifshitz-Slonczewski equation\nby Chunxi Jiao (University of Sydney) as part of Sydney Dynamics Group Semina r\n\n\nAbstract\nWe study a stochastic Landau-Lifshitz-Slonczewski equatio n on the real line with one-dimensional noise. We show that there exists a pathwise unique solution to this equation for small noises and discuss th e regularity of the solution. The proof is based on a discrete approximati on followed by a quadratic interpolation with some uniform estimates\, and we adapt arguments in Brzeźniak\, Goldys and Jegaraj (2012) for converge nce results.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Meagan Carney (University of Queensland) DTSTART;VALUE=DATE-TIME:20211105T050000Z DTEND;VALUE=DATE-TIME:20211105T060000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/27 DESCRIPTION:Title: Nonstationary extremal modeling in weather systems\nby Meagan Carn ey (University of Queensland) as part of Sydney Dynamics Group Seminar\n\n \nAbstract\nExtremes in weather can often take the form of a hurricane\, f lood\, or heat-wave. A better understanding of how large and frequent thes e events will be can influence evacuation procedures and inform preventati ve measures. We briefly discuss modeling extremes of dynamical systems in the classical i.i.d. setting. Classical results of extreme value theory ex tend naturally to dependent sequences provided the distribution of the seq uence is stationary. In recent years\, climate variability has caused chan ges in the distribution of weather observations. For example\, we have sho wn that the mean and standard deviation of summer temperature extremes in Texas and Germany is increasing over time. We finish by discussing how mac hine learning techniques can allow us to obtain more accurate\, time-depen dent extremal models in these settings.\n\nEmail the organiser directly fo r the Zoom link.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Courtney Quinn (CSIRO (Hobart)) DTSTART;VALUE=DATE-TIME:20211008T050000Z DTEND;VALUE=DATE-TIME:20211008T060000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/28 DESCRIPTION:Title: Dynamical analysis of data-driven reduced models for persistent atmosp heric states\nby Courtney Quinn (CSIRO (Hobart)) as part of Sydney Dyn amics Group Seminar\n\n\nAbstract\nWhile clustering techniques are highly useful in identifying regimes of large-dimensional data\, some methods (su ch as FEM-BV-VAR) also produce time-dependent models for the corresponding regime dynamics. We investigate these reduced models in the context of c limate regimes\, where the FEM-BV-VAR methodology is applied to atmospheri c reanalysis data of different regions. To analyse the dynamics we use a method for computing the covariant Lyapunov vectors (CLVs) over various ti me windows\, where short windows produce a set of mixed singular vectors ( MSVs) and longer windows approximate the asymptotic CLVs. The growth rates and alignment of the resulting time-dependent vectors are then compared\, with a particular focus on indicators of transitions between the states. We find that the window chosen to compute the vectors acts as a filter\, w ith short windows capturing the dynamics of individual transitions and lon g windows identifying low-frequency variability. We then compare the prop erties of MSVs to those of traditional singular vectors and relate to thei r application in ensemble numerical weather prediction (NWP). We show that MSVs provide a systematic approach to generate initial forecast perturbat ions projected onto relevant expanding directions in phase space for typic al NWP forecast lead-times.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrus Girlado (University of Auckland) DTSTART;VALUE=DATE-TIME:20211022T040000Z DTEND;VALUE=DATE-TIME:20211022T050000Z DTSTAMP;VALUE=DATE-TIME:20230208T064501Z UID:SDGSeminar/29 DESCRIPTION:Title: Degenerate singular cycles and chaotic switching in the two-site open Bose--Hubbard model\nby Andrus Girlado (University of Auckland) as par t of Sydney Dynamics Group Seminar\n\n\nAbstract\nThe two-site open Bose-H ubbard dimer model is a celebrated fundamental quantum optical model that accounts for the dynamics of bosons at two lossy interacting sites. Recent ly\, two coupled\, driven\, and lossy photonic crystal nanocavities ---whi ch are optical devices that operate with only a few hundred photons due to their extremely small size--- have been shown to realise this model exper imentally. Thus\, there is much interest in understanding the different be haviours that such model exhibits for theoretical and practical purposes.\ n\nThis talk will show the different dynamics in the semiclassical approxi mation of this quantum optical system by presenting a comprehensive bifurc ation analysis. We characterised different transitions of chaotic attracto rs in parameter plane by numerically computing tangency bifurcations betwe en stable and unstable manifolds of saddle equilibria and periodic orbits. By doing so\, we identify codimension-two degenerate singular cycles\, an d their generalisations\, as responsible for the organisations of differen t tangency and heteroclinic bifurcations between saddle equilibria periodi c orbits in parameter plane. Thus\, we provide a roadmap for observable ch aotic dynamics in the semiclassical approximation of the two-site Bose-Hub bard dimer model\, which connects novel results in bifurcation theory with novel applications through numerical continuation techniques.\n\nEmail th e organisers for the Zoom link.\n LOCATION:https://researchseminars.org/talk/SDGSeminar/29/ END:VEVENT END:VCALENDAR