Dynamical Systems Commons^™

Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, Scott R. Kaschner, Reaper Romero, David Simmons

Scholarship and Professional Work - LAS

We show that the geometric limit as n → ∞ of the Julia sets J(P_n,c) for the maps P_n,c(z) = zⁿ + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.

Superstable Manifolds Of Invariant Circles And Codimension-One Böttcher Functions, Scott R. Kaschner, Roland K.W. Roeder

Scholarship and Professional Work - LAS

Let f:X ⇢ X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n>1. Suppose that there is an embedded copy of P1 that is invariant under f, with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose that f restricted to this line is given by z↦zb, with resulting invariant circle S. We prove that if a≥b, then the local stable manifold Wsloc(S) is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show that the condition …

Inżynieria Chemiczna Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

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Tematyka Prac Doktorskich, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Control, Stability, And Qualitative Theory Of Dynamical Systems 2014, Nazim I. Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren

Mathematics Faculty Publications

No abstract provided.

Symbolic Neutrosophic Theory, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Symbolic (or Literal) Neutrosophic Theory is referring to the use of abstract symbols (i.e. the letters T, I, F, or their refined indexed letters T_j, I_k, F_l) in neutrosophics.

In the first chapter we extend the dialectical triad thesis-antithesis-synthesis (dynamics of A and antiA, to get a synthesis) to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis (dynamics of A, antiA, and neutA, in order to get a neutrosynthesis).

In the second chapter we introduce the neutrosophic system and neutrosophic dynamic system. A neutrosophic system is a quasi- or –classical system, in the sense that the neutrosophic …

Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan

Theses and Dissertations

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.

We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation …

Rational Maps Of Cp^2 With No Invariant Foliation, Scott R. Kaschner, Rodrigo A. Perez, Roland K.W. Roeder

Scholarship and Professional Work - LAS

We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation.

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities …

Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya

Mathematics and Statistics Faculty Publications and Presentations

We propose methodology for exact statistical tests of hypotheses for models of network dynamics. The methodology formulates Markovian exponential families, then uses sequential importance sampling to compute expectations within basins of attraction and within level sets of a sufficient statistic for an over-dispersion model. Comparisons of hypotheses can be done conditional on basins of attraction. Examples are presented.

Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds, Robert J. Kipka

Dissertations

Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds Driven by applications in fields such as robotics and satellite attitude control, as well as by a need for the theoretical development of appropriate tools for the analysis of geometric systems, problems of control of dynamical systems on manifolds have been studied intensively during the past three decades. In this dissertation we suggest new mathematical techniques for the study of control and dynamic optimization problems on manifolds. This work has several components including: an extension of the classical Chronological Calculus to control and dynamical systems which are merely …

Vanishing Configurations In Network Dynamics With Asynchronous Updates, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

We consider Boolean dynamics for biological networks where stochasticity is introduced through asynchronous updates. An exact method is given for finding states which can reach a steady state with positive probability, and a method is given for finding states which cannot reach other steady states. These methods are based on computational commutative algebra. The algorithms are applied to dynamics of a cell survival network to determine node assignments that exclude termination in a cancerous state

Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde

Mathematics Faculty Research

Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diffusion coefficient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, sufficient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure …

Bayes, Brains & Babies: Electrophysiology And Mathematics Of Infant Holistic Processing And Selective Inhibition, Matthew Singh

EURēCA: Exhibition of Undergraduate Research and Creative Achievement

No abstract provided.

Dynamics Of Traveling Waves In Neural Networks In Presence Of Period Inhomogeneities, Rosahn Bhattarai

Georgia State Undergraduate Research Conference

No abstract provided.

Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov

Conference papers

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g^∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of different G-strand …

Fractal Powers In Serrin's Swirling Vortex Solutions, Pavel Bělík, Douglas P. Dokken, Kurt Scholz, Mikhail M. Shvartsman

Faculty Authored Articles

We consider a modification of the fluid flow model for a tornado-like swirling vortex developed by Serrin [Phil. Trans. Roy. Soc. London, Series A, Math & Phys. Sci. 271(1214) (1972), 325–360], where velocity decreases as the reciprocal of the distance from the vortex axis. Recent studies, based on radar data of selected severe weather events [Mon. Wea. Rev. 133(9) (2005), 2535–2551; Mon. Wea. Rev. 128(7) (2000), 2135–2164; Mon. Wea. Rev. 133(1) (2005), 97–119], indicate that the angular momentum in a tornado may not be constant with the radius, and thus suggest a different scaling of the velocity/radial distance dependence. Motivated …

Can A Falling Bullet Kill You?, Zechariah Thurman

Zechariah Thurman

A terminal velocity examination of the problem of the falling bullet is investigated.

Termodynamika Procesowa I Techniczna Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.