Quispel, Two classes of quadratic vector fields for which the Kahan discretization is integrable, MI Lecture Notes , 74 , 60— Quispel, Integrability properties of Kahan's method, J. A , 47 , Cossec and I. Haggar , G. Byrnes , G. Quispel and H. A , , Hirota , K. Kimura and H. Yahagi , How to find conserved quantities of nonlinear discrete equations, J. A , 34 , Hitchin , N. Manton and M. Murray , Symmetric monopoles, Nonlinearity , 8 , Iatrou and J.
Roberts , Integrable mappings of the plane preserving biquadratic invariant curves, J. Jogia , J. Roberts and F. Vivaldi , An algebraic geometric approach to integrable maps of the plane, J. A , 39 , Joshi , B.
Grammaticos , T. Tamizhmami and A. Kassotakis and N. Kimura , H. Yahagi , R. Hirota , A. Ramani , B. Grammaticos and Y. Ohta , A new class of integrable discrete systems, J. A , 35 , Lyness, Note , Math. Manin , The Tate height of points on an Abelian variety. Moody , Notes on the Bertini involution, Bull. Petrera , A. Pfadler and Y. Suris , On integrability of Hirota-Kimura type discretizations, Regul.
Chaotic Dyn. Petrera, J. Smirin and Y. Suris, Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems, Proc. Petrera and Y. Suris , Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems. Systems with a linear Poisson tensor, J. Suris, Manin involutions for elliptic pencils and discrete integrable systems, arXiv: Quispel , J. Roberts and C.
Thompson , Integrable mappings and soliton equations, Phys. Roberts and G. Quispel , Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems, Phys.
Sakkalis and R. Farouki , Singular points of algebraic curves, J. Symbolic Comput. Silverman and J.
Tsuda , Integrable mapping via rational elliptic surfaces, J. A , 37 , Quispel, Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation, J. A: Math. Monthly , , Veselov , Integrable mappings, Russ. Viallet , B. Grammaticos and A. Ramani , On the integrability of correspondences associated to integral curves, Phys. Download as PowerPoint slide.
Nalini Joshi , Pavlos Kassotakis. Re-factorising a QRT map. Journal of Computational Dynamics , , 6 2 : Sangtae Jeong , Chunlan Li. Measure-preservation criteria for a certain class of 1-lipschitz functions on Z p in mahler's expansion. Colin J. Cotter , Michael John Priestley Cullen. Particle relabelling symmetries and Noether's theorem for vertical slice models. Journal of Geometric Mechanics , , 11 2 : Nimish Shah , Lei Yang. Equidistribution of curves in homogeneous spaces and Dirichlet's approximation theorem for matrices.
John Hubbard , Yulij Ilyashenko. A proof of Kolmogorov's theorem. Rabah Amir , Igor V. On Zermelo's theorem. Virginia Agostiniani , Rolando Magnanini. Symmetries in an overdetermined problem for the Green's function. Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems. Journal of Geometric Mechanics , , 10 2 : Conley's theorem for dispersive systems.
Sergei Ivanov. On Helly's theorem in geodesic spaces. Electronic Research Announcements , , Hsuan-Wen Su. Finding invariant tori with Poincare's map. Amadeu Delshams , Josep J. Computing the scattering map in the spatial Hill's problem. Ugo Bessi. Another point of view on Kusuoka's measure. Florio M. Schwinger's picture of quantum mechanics: 2-groupoids and symmetries. Journal of Geometric Mechanics , , 13 3 : Pengyan Wang , Pengcheng Niu.
Liouville's theorem for a fractional elliptic system. Firstly, suppose that W and U are isomorphic H -modules. The second possibility is that W and U are non-isomorphic H -modules. Indeed, we may invert h U and h W individually, and we may also swap the blocks h U and h W. Thus we have. Now suppose that h acts trivially on U and U t. This results in. Then there are two subcases to consider. This occurs if and only if h takes the form. For each such h , we have. Hence we have. However, this of course just yields the identity element, and adds 1 to the count.
We wish to consider certain subgroups of G having profiles which are in some sense maximal. We then define. Subgroups with profiles in MProf will contain elements which, when block diagonalized, contain no trivial Jordan blocks. We repeat the definition of such subgroups from Section 2. First we consider those elements of H which satisfy i. Thus we require that g has order coprime to q k i - 1. Now consider those elements of H which satisfy ii.
Finally, consider those elements of H which satisfy iii. This number does not depend on q , so for q sufficiently large, there are q k i choices of h j. Hence the number of elements of H which satisfy iii is given by a polynomial with leading term q k. Now we apply Lemmas 2. In view of Lemma 4. Moreover, by Lemma 4. Putting this together, we see that. As preparation for the proof of Proposition 4.
The first is [ 11 , identity 3. Continuing, we see that there are. We may therefore apply Lemma 4. Now, using the fact that. The proof of Theorem 1. Within K , we may consider t to be an involution with maximal rank. By Lemma 4. Therefore, arguing as previously, we have that. Aschbacher and G. Seitz, Involutions in Chevalley groups over fields of even order, Nagoya Math.
Search in Google Scholar. Ballantyne, Local fusion graphs of finite groups, PhD. Thesis, University of Manchester, Ballantyne, N. Greer and P. Rowley, Local fusion graphs for symmetric groups, J.
Group Theory 16 , no. Ballantyne and P. Rowley, A note on computing involution centralizers, J. Symbolic Comput. Rowley, Local fusion graphs and sporadic simple groups, Electron. Ballantyne, On local fusion graphs of finite Coxeter groups, J.
Borovik and C. Algebra , — Bray, An improved method for generating the centralizer of an involution, Arch. Basel 74 , no. Devillers and M. Giudici, Involution graphs where the product of two adjacent vertices has order three, J. Gorenstein, Finite Groups, 2nd ed. Gould, Combinatorial Identities, revised ed. Guralnick and F. Huppert, Endliche Gruppen. I, Grundlehren Math. Kantor and M.
Algebra , 16— Kleidman and M. Lecture Note Ser. Liebeck, On products of involutions in finite groups of Lie type in even characteristic, J. Parker and R. Wilson, Recognising simplicity of black-box groups by constructing involutions and their centralisers, J. Algebra , no. Your documents are now available to view. Confirm Cancel. John J. Ballantyne and Peter J.
From the journal Journal of Group Theory. Cite this. Lemma 2. Involutions in G are G -conjugate if and only if they have equal rank. Definition 2. Theorem 2. Definition 4. Lemma 4. Proposition 4. Proof of Proposition 4. Received:
0コメント