Last edited by Guktilar
Wednesday, May 13, 2020 | History

2 edition of Bifurcation into spectral gaps found in the catalog.

Bifurcation into spectral gaps

Charles A Stuart

# Bifurcation into spectral gaps

## by Charles A Stuart

Written in English

Subjects:
• Bifurcation theory,
• Spectral theory (Mathematics),
• Differential equations, Nonlinear -- Numerical solutions

• Edition Notes

The Physical Object ID Numbers Other titles Bulletin of the Belgian Mathematical Society. Supplement Statement Charles A. Stuart Pagination 59 p. ; Number of Pages 59 Open Library OL14983636M

In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalues of a matrix or operator; alternately, it is sometimes taken as the smallest non-zero eigenvalue. Various theorems relate this difference to other properties of the system. See: Expander graph (discrete case); Poincaré inequality (continuous case); See also. An Adaptive Minimum Spanning Tree Multielement Method for Uncertainty Quantification of Smooth and Discontinuous Responses Mathematics Applied to Deterministic Problems in the Natural Sciences (C. C. Lin and L. A. Segel)Cited by: 1.

Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations - Kindle edition by Kirillov, Oleg N., Pelinovsky, Dmitry E.. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Nonlinear Physical Systems: Spectral Analysis, Stability and cturer: Wiley-ISTE. Bifurcations and stability of gap solitons in periodic potentials Dmitry E. Pelinovsky,1 Andrey A. Sukhorukov,2 and Yuri S. Kivshar2 1Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 2Nonlinear Physics Group and Centre for Ultra-high Bandwidth Devices for Optical Systems (CUDOS), Research School of Physical Sciences and Engineering, Australian .

The spectral gap—the energy difference between the ground state and first excited state of a system—is central to quantum many-body physics. Many Cited by: Lecture Notes on Expansion, Sparsest Cut, and Spectral Graph Theory Luca Trevisan University of California, BerkeleyFile Size: KB.

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### Bifurcation into spectral gaps by Charles A Stuart Download PDF EPUB FB2

Bifurcation into spectral gaps. [Charles A Stuart] Bifurcation theory. Spectral theory (Mathematics) Differential equations, Nonlinear -- Numerical solutions. Book: All Authors / Contributors: Charles A Stuart. Find more information about: OCLC Number: In this lecture bifurcation from any boundary point of the essential spectrum is studied for a class of nonlinear operators generalizing results concerning Bifurcation into spectral gaps book from the lowest point of the Bifurcation Into Gaps in the Essential Bifurcation into spectral gaps book | SpringerLinkCited by: BIFURCATION INTO SPECTRAL GAPS FOR A NONCOMPACT SEMILINEAR SCHRÖDINGER EQUATION WITH NONCONVEX POTENTIAL TROESTLER C.

Abstract. This paper shows that the nonlinear periodic eigenvalue problem (−∆u + V (x)u − f(x,u) = λu, u ∈ H1(RN), has a nontrivial branch of solutions emanating from the upper bound of every spectral gap of −∆ + V.

Assuming that ]a, b[ is a spectral gap of the combined spectrum ρ(A, L):= {λ ∈ IR: A − λL: H → H is an isomorphism} we show that λ = b is a bifurcation point for (P). This paper shows that the nonlinear periodic eigenvalue problem $${cases} -\Delta u + V(x) u - f(x,u) = \lambda u, u \in H^1(\IR^N), {cases}$$ has a nontrivial branch of solutions emanating from the upper bound of every spectral gap of $-\Delta + V$.Cited by: 6.

Stuart, Charles Alexander. Bulletin of the Belgian Mathematical Society - Simon Stevin, Suppl., 59Cited by:   Title: Bifurcation into spectral gaps for a noncompact semilinear Schrödinger equation with nonconvex potential Authors: Christophe Troestler (Submitted on 4 Jul )Cited by: 6.

A variational approach to bifurcation into spectral gaps Article (PDF Available) in Annali della Scuola normale superiore di Pisa, Classe di scienze 28(4) January with 26 Reads. Journal für die Reine und Angewandte Mathematik,Year: Cited by: Lecture The Spectral Gap We deﬁne Hx t(y) = H(x,y), which is a probability measure on X specifying the distribution at time tof a continuous time Markov chain (X t) t>0 with transition matrix Kstarting from x.

Conceptually, the process (X t) may be described as have a Poisson clock which rings according to a. Bifurcation into spectral gaps for a noncompact semilinear Schr\"odinger equation with nonconvex potential. u \in H^1(\IR^N), {cases} has a nontrivial branch of solutions emanating from the upper bound of every spectral gap of $-\Delta + V$.

No convexity condition is assumed. The following result of independent interest is also proven Author: Christophe Troestler. Stuart C.A.

() Bifurcation from the Essential Spectrum. In: Matzeu M., Vignoli A. (eds) Topological Nonlinear Analysis II. Progress in Nonlinear Differential Equations and Cited by:   The quantum mechanical effects of bifurcation have also been reported in the study of short-range spectral correlations.

Makino, Harayama, and Aizawa investigated numerically the nearest-neighbor level-spacing distribution (NNLSD) in the quantum oval billiard and found anomalous accumulation of adjacent levels at the bifurcation point where the Author: Hironori Makino.

Preface to the Second Edition The favorable reaction to the ﬁrst edition of this book conﬁrmed that the publication of such an application-oriented text on bifurcation theory of dynamical systems was well timed.

The selected topics indeed cover ma-jor practical issues of applying the bifurcation theory to ﬁnite-dimensional problems. () For one thing, the existence of spectral gaps is the rule rather than the exception in the periodic case (cf.

[15, 16]), and, for another, special information available for the spectral theory of periodic Schringer operators makes it possible to use the results and methods from Section 3 more efficiently than in the general by: 8.

When G = (a, b) is a spectral gap for S, we set HG:= E(a)H, (13) where [E.1): A E R) is the right-continuous resolution of the identity associated with S.

Thus Ho is the range of the spectral projection PG = E(a): H - H, and we note that PG restricted to Hl is the orthogonal projection in Hl of Hl onto by: Actual research concerning, in particular, the occurrence of "gap-solitons" bifurcating from the continuous spectrum confirms that this part of Bifurcation Theory that started around 40 years ago flourishes.

In this lecture we review the origins of "Bifurcation from the continuous spectrum" with regard to the achievements of Jürgen Scheurle and sketch how the early results dealing with the Author: Tassilo Küpper. (at least temporarily) ﬁll in the possible gaps in the background of the prospective Master’s level reader.

The goal of this book is to begin with the basics of normed linear spaces, quickly specialise to Hilbert spaces and to get to the spectral theorem for (bounded as.

Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering.

of a “spectral gap.” These proofs can be extended to inﬁnite dimensions. In particular, the applications of the ﬁber contraction principle and the Lyapunov–Perron method in this book provide an introduction to some of the basic tools of invariant manifold theory.

The theory of averaging is treated from a fresh perspective that is in-Cited by:. Recommend & Share. Recommend to Library. Email to a friendCited by: into a continuous power histogram. The vertical axis shows frequency, while the color indicates the power at that frequency.

Comparing the spectral bifurcation diagram with Figures 1 and the upper two panels, we see that the lines beginning at and after and continuing to represent the periodic Size: KB.used textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, c ).

Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven.