@inbook{16553, author = {{Dellnitz, Michael and Froyland, Gary and Sertl, Stefan}}, booktitle = {{Equadiff 99}}, isbn = {{9789810243593}}, title = {{{A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator}}}, doi = {{10.1142/9789812792617_0199}}, year = {{2000}}, } @article{16554, author = {{Dellnitz, Michael and Froyland, Gary and Sertl, Stefan}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, pages = {{1171--1188}}, title = {{{On the isolated spectrum of the Perron-Frobenius operator}}}, doi = {{10.1088/0951-7715/13/4/310}}, year = {{2000}}, } @inbook{16616, author = {{Junge, Oliver}}, booktitle = {{Equadiff 99}}, isbn = {{9789810243593}}, title = {{{Rigorous discretization of subdivision techniques}}}, doi = {{10.1142/9789812792617_0178}}, year = {{2000}}, } @inbook{17018, author = {{Dellnitz, Michael and Junge, Oliver and Rumpf, Martin and Strzodka, Robert}}, booktitle = {{Equadiff 99}}, isbn = {{9789810243593}}, pages = {{1053----1059}}, title = {{{The computation of an unstable invariant set inside a cylinder containing a knotted flow}}}, doi = {{10.1142/9789812792617_0204}}, year = {{2000}}, } @article{34900, abstract = {{We describe methods for the computation of Galois groups of univariate polynomials over the rationals which we have implemented up to degree 15. These methods are based on Stauduhar’s algorithm. All computations are done in unramified p -adic extensions. For imprimitive groups we give an improvement using subfields. In the primitive case we use known subgroups of the Galois group together with a combination of Stauduhar’s method and the absolute resolvent method.}}, author = {{Geissler, Katharina and Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{6}}, pages = {{653--674}}, publisher = {{Elsevier BV}}, title = {{{Galois Group Computation for Rational Polynomials}}}, doi = {{10.1006/jsco.2000.0377}}, volume = {{30}}, year = {{2000}}, } @article{34901, abstract = {{Let L = K(α) be an Abelian extension of degree n of a number field K, given by the minimal polynomial of α over K. We describe an algorithm for computing the local Artin map associated with the extension L / K at a finite or infinite prime v of K. We apply this algorithm to decide if a nonzero a ∈ K is a norm from L, assuming that L / K is cyclic.}}, author = {{Acciaro, Vincenzo and Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{3}}, pages = {{239--252}}, publisher = {{Elsevier BV}}, title = {{{Computing Local Artin Maps, and Solvability of Norm Equations}}}, doi = {{10.1006/jsco.2000.0361}}, volume = {{30}}, year = {{2000}}, } @article{34899, abstract = {{We describe methods for the construction of polynomials with certain types of Galois groups. As an application we deduce that all transitive groups G up to degree 15 occur as Galois groups of regular extensions of ℚ (t), and in each case compute a polynomial f ∈ ℚ [ x ] with Gal(f) = G.}}, author = {{Klüners, Jürgen and Malle, Gunter}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{6}}, pages = {{675--716}}, publisher = {{Elsevier BV}}, title = {{{Explicit Galois Realization of Transitive Groups of Degree up to 15}}}, doi = {{10.1006/jsco.2000.0378}}, volume = {{30}}, year = {{2000}}, } @article{34898, abstract = {{We compute a polynomial with Galois group SL₂(11) over ℚ. Furthermore we prove that SL₂(11) is the Galois group of a regular extension of ℚ (t).}}, author = {{Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{6}}, pages = {{733--737}}, publisher = {{Elsevier BV}}, title = {{{A Polynomial with Galois GroupSL2(11)}}}, doi = {{10.1006/jsco.2000.0380}}, volume = {{30}}, year = {{2000}}, } @article{16511, author = {{Aston, Philip J. and Dellnitz, Michael}}, issn = {{0045-7825}}, journal = {{Computer Methods in Applied Mechanics and Engineering}}, pages = {{223--237}}, title = {{{The computation of lyapunov exponents via spatial integration with application to blowout bifurcations}}}, doi = {{10.1016/s0045-7825(98)00196-0}}, year = {{1999}}, } @article{16537, author = {{Dellnitz, Michael and Junge, Oliver}}, issn = {{0036-1429}}, journal = {{SIAM Journal on Numerical Analysis}}, pages = {{491--515}}, title = {{{On the Approximation of Complicated Dynamical Behavior}}}, doi = {{10.1137/s0036142996313002}}, year = {{1999}}, } @inbook{16584, author = {{Deuflhard, Peter and Dellnitz, Michael and Junge, Oliver and Schütte, Christof}}, booktitle = {{Computational Molecular Dynamics: Challenges, Methods, Ideas}}, isbn = {{9783540632429}}, issn = {{1439-7358}}, title = {{{Computation of Essential Molecular Dynamics by Subdivision Techniques}}}, doi = {{10.1007/978-3-642-58360-5_5}}, year = {{1999}}, } @article{17017, author = {{Bürkle, David and Dellnitz, Michael and Junge, Oliver and Rumpf, Martin and Spielberg, Michael}}, journal = {{Proceedings of Visualization 99}}, title = {{{Visualizing Complicated Dynamics}}}, year = {{1999}}, } @article{34902, abstract = {{We present a new polynomial decomposition which generalizes the functional and homogeneous bivariate decomposition of irreducible monic polynomials in one variable over the rationals. With these decompositions it is possible to calculate the roots of an imprimitive polynomial by solving polynomial equations of lower degree.}}, author = {{Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{3}}, pages = {{261--269}}, publisher = {{Elsevier BV}}, title = {{{On Polynomial Decompositions}}}, doi = {{10.1006/jsco.1998.0252}}, volume = {{27}}, year = {{1999}}, } @article{35941, abstract = {{Let L = ℚ(α) be an abelian number field of degree n. Most algorithms for computing the lattice of subfields of L require the computation of all the conjugates of α. This is usually achieved by factoring the minimal polynomial mα(x) of α over L. In practice, the existing algorithms for factoring polynomials over algebraic number fields can handle only problems of moderate size. In this paper we describe a fast probabilistic algorithm for computing the conjugates of α, which is based on p-adic techniques. Given mα(x) and a rational prime p which does not divide the discriminant disc(mα(x)) of mα(x), the algorithm computes the Frobenius automorphism of p in time polynomial in the size of p and in the size of mα(x). By repeatedly applying the algorithm to randomly chosen primes it is possible to compute all the conjugates of α.}}, author = {{Klüners, Jürgen and Acciaro, Vincenzo}}, issn = {{1088-6842}}, journal = {{Mathematics of Computation}}, number = {{227}}, pages = {{1179--1186}}, publisher = {{American Mathematical Society (AMS)}}, title = {{{Computing Automorphisms of Abelian Number Fields}}}, volume = {{68}}, year = {{1999}}, } @article{16536, author = {{Dellnitz, Michael and Junge, Oliver}}, issn = {{1432-9360}}, journal = {{Computing and Visualization in Science}}, pages = {{63--68}}, title = {{{An adaptive subdivision technique for the approximation of attractors and invariant measures}}}, doi = {{10.1007/s007910050006}}, year = {{1998}}, } @article{16535, abstract = {{ Recently multilevel subdivision techniques have been introduced in the numerical investigation of complicated dynamical behavior. We illustrate the applicability and efficiency of these methods by a detailed numerical study of Chua's circuit. In particular we will show that there exist two regions in phase space which are almost invariant in the sense that typical trajectories stay inside each of these sets on average for quite a long time. }}, author = {{Dellnitz, Michael and Junge, Oliver}}, issn = {{0218-1274}}, journal = {{International Journal of Bifurcation and Chaos}}, pages = {{2475--2485}}, title = {{{Almost Invariant Sets in Chua's Circuit}}}, doi = {{10.1142/s0218127497001655}}, year = {{1997}}, } @article{16552, author = {{Dellnitz, Michael and Hohmann, Andreas and Junge, Oliver and Rumpf, Martin}}, issn = {{1054-1500}}, journal = {{Chaos: An Interdisciplinary Journal of Nonlinear Science}}, pages = {{221--228}}, title = {{{Exploring invariant sets and invariant measures}}}, doi = {{10.1063/1.166223}}, year = {{1997}}, } @article{16614, author = {{Guder, Rabbijah and Dellnitz, Michael and Kreuzer, Edwin}}, issn = {{0960-0779}}, journal = {{Chaos, Solitons & Fractals}}, pages = {{525--534}}, title = {{{An adaptive method for the approximation of the generalized cell mapping}}}, doi = {{10.1016/s0960-0779(96)00118-x}}, year = {{1997}}, } @article{17015, author = {{Dellnitz, Michael and Hohmann, Andreas}}, issn = {{0029-599X}}, journal = {{Numerische Mathematik}}, pages = {{293--317}}, title = {{{A subdivision algorithm for the computation of unstable manifolds and global attractors}}}, doi = {{10.1007/s002110050240}}, volume = {{75}}, year = {{1997}}, } @article{34903, abstract = {{The software packageKANT V4for computations in algebraic number fields is now available in version 4. In addition a new user interface has been released. We will outline the features of this new software package.}}, author = {{DABERKOW, M. and FIEKER, C. and Klüners, Jürgen and POHST, M. and ROEGNER, K. and SCHÖRNIG, M. and WILDANGER, K.}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{3-4}}, pages = {{267--283}}, publisher = {{Elsevier BV}}, title = {{{KANT V4}}}, doi = {{10.1006/jsco.1996.0126}}, volume = {{24}}, year = {{1997}}, }