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1.
Sylvain Crovisier 《Advances in Mathematics》2011,(1):673
We prove that any diffeomorphism of a compact manifold can be C1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially hyperbolic (its chain-recurrent set splits into partially hyperbolic pieces whose centre bundles have dimensions less or equal to two). We also study in a more systematic way the central models introduced in Crovisier (in press) [10]. 相似文献
2.
In this paper we dramatically expand the domain of known stably ergodic, partially hyperbolic dynamical systems. For example,
all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property are stably
ergodic. Our main tools are the new concepts – julienne density point and julienne quasi-conformality of the stable and unstable
holonomy maps. Julienne quasi-conformal holonomy maps preserve all julienne density points.
Received June 14, 1999 / final version received October 25, 1999 相似文献
3.
Javier Ribón 《Journal of Differential Equations》2012,253(12):3211-3231
In [Xiang Zhang, The embedding flows of C∞ hyperbolic diffeomorphisms, J. Differential Equations 250 (5) (2011) 2283-2298] Zhang proved that any local smooth hyperbolic diffeomorphism whose eigenvalues are weakly nonresonant is embedded in the flow of a smooth vector field. We present a new and more conceptual proof of such result using the Jordan-Chevalley decomposition in algebraic groups and the properties of the exponential operator.We characterize the hyperbolic smooth (resp. formal) diffeomorphisms that are embedded in a smooth (resp. formal) flow. We introduce a criterion showing that the presence of weak resonances for a diffeomorphism plus two natural conditions imply that it is not embeddable. This solves a conjecture of Zhang. The criterion is optimal, we provide a method to construct embeddable diffeomorphisms with weak resonances if we remove any of the conditions. 相似文献
4.
Manseob Lee 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):689-694
Let p be a hyperbolic periodic saddle of a diffeomorphism of f on a closed smooth manifold M, and let Hf(p) be the homoclinic class of f containing p. In this paper, we show that if Hf(p) is locally maximal and every hyperbolic periodic point in Hf(p) is uniformly far away from being nonhyperbolic, and Hf(p) has the average shadowing property, then Hf(p) is hyperbolic. 相似文献
5.
Let
be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We find several criteria for transitivity of noncompact connected Lie group extensions. As a consequence, we find transitive extensions for any finite-dimensional connected Lie group extension. If, in addition, the group is perfect and has an open set of elements that generate a compact subgroup, we find open sets of stably transitive extensions. In particular, we find stably transitive
-extensions. More generally, we find stably transitive
-extensions for all n ≥ 1. For the Euclidean groups SE(n) with n ≥ 4 even, we obtain a new proof of a result of Melbourne and Nicol stating that there is an open and dense set of extensions that are transitive.For groups of the form
where K is compact, a separation condition is necessary for transitivity. Provided X is a hyperbolic attractor, we show that an open and dense set of extensions satisfying the separation condition are transitive. This generalizes a result of Niţică and Pollicott for
-extensions.Communicated by Viviane Baladisubmitted 24/05/04, accepted 11/10/04 相似文献
6.
Yoshinobu Kamishima 《Geometriae Dedicata》2006,122(1):33-49
Long and Reid [Algebr. Geom. Topol. 2: 285–296, 2002] have shown that the diffeomorphism class of every Riemannian flat manifold
of dimension n≥ 3 arises as a cusp cross-section of a complete finite volume real hyperbolic (n+1)-orbifold. For the complex hyperbolic case, McReynolds [Algebr. Geom. Topol. 4: 721–755, 2004] proved that every 3-dimensional
infranilmanifold is diffeomorphic to a cusp cross-section of a complete finite volume complex hyperbolic 2-orbifold. Moreover,
he gave a necessary and sufficient condition for a Heisenberg infranilmanifold to be realized as a cusp cross-section of finite
volume (arithmetically) complex hyperbolic orbifold. We study these realization problems by using Seifert fibrations. 相似文献
7.
We give a complete invariant, called global scheme, of topological conjugacy classes of gradient-like diffeomorphisms, on compact 3-manifolds. Conversely, we can realize any abstract global scheme by such a diffeomorphism. 相似文献
8.
Martin Grohe 《Combinatorica》1999,19(4):507-532
of first-order logic whose formulas contain at most k variables (for some ). We show that for each , equivalence in the logic is complete for polynomial time. Moreover, we show that the same completeness result holds for the powerful extension of with counting quantifiers (for every ).
The k-dimensional Weisfeiler–Lehman algorithm is a combinatorial approach to graph isomorphism that generalizes the naive color-refinement
method (for ). Cai, Fürer and Immerman [6] proved that two finite graphs are equivalent in the logic if, and only if, they can be distinguished by the k-dimensional Weisfeiler-Lehman algorithm. Thus a corollary of our main result is that the question of whether two finite graphs
can be distinguished by the k-dimensional Weisfeiler–Lehman algorithm is P-complete for each .
Received: March 23, 1998 相似文献
9.
This article is a rigorous study of the dual pair structure of the ideal fluid (Phys D 7:305–323, 1983) and the dual pair structure for the n-dimensional Camassa–Holm (EPDiff) equation (The breadth of symplectic and poisson geometry: Festshrift in honor of Alan Weinstein,
2004), including the proofs of the necessary transitivity results. In the case of the ideal fluid, we show that a careful definition
of the momentum maps leads naturally to central extensions of diffeomorphism groups such as the group of quantomorphisms and
the Ismagilov central extension. 相似文献
10.
D. V. Treshchev 《Mathematical Notes》1997,61(6):744-757
Generally, the invariant Lagrangian manifolds (stable and unstable separatrices) asymptotic with respect to a hyperbolic torus
of a Hamiltonian system do not coincide. This phenomenon is called separatrix splitting. In this paper, a symplectic invariant
qualitatively describing separatrix splitting for hyperbolic tori of maximum (smaller by one than the number of degrees of
freedom) dimension is constructed. The construction resembles that of the homoclinic invariant found by lazutkin for two-dimensional
symplectic maps and of Bolotin's invariant for splitting of asymptotic manifolds of a fixed point of a symplectic diffeomorphism.
Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 890–906, June, 1997.
Translated by O. V. Sipacheva 相似文献
11.
We study the ergodic theory of non-conservative C
1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose
supports coincide with the homoclinic class. Second, we show that generic (for the weak topology) ergodic measures of C
1-generic diffeomorphisms are non-uniformly hyperbolic: they exhibit no zero Lyapunov exponents. Third, we extend a theorem
by Sigmund on hyperbolic basic sets: every isolated transitive set Λ of any C
1-generic diffeomorphism f exhibits many ergodic hyperbolic measures whose supports coincide with the whole set Λ. 相似文献
12.
In this note, we introduce the notion of nonuniformly sectional hyperbolic set and use it to prove that any C1-open set which contains a residual subset of vector fields with nonuniformly sectional hyperbolic critical set also contains a residual subset of vector fields with sectional hyperbolic nonwandering set. This not only extends Theorem A of Castro [11], but using suspensions we recover it. 相似文献
13.
C. Zălinescu 《Mathematical Methods of Operations Research》2008,68(3):493-508
Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction
version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing
results. Then we derive the Yang extension theorem using a similar proof as well as a stronger version of it using a classical
separation theorem. Moreover, we give counterexamples to several extension theorems stated in the literature.
Dedicated to Jean-Paul Penot with the occasion of his retirement. 相似文献
14.
Wenli Liu 《Linear and Multilinear Algebra》2013,61(4):527-542
We introduce a new technique, called the T?*-extension, of constructing metric n-Lie algebras from arbitrary ones and obtain some important properties on this extension. Finally, we investigate the metric n-Lie algebras that are isometric to certain T?*-extensions. 相似文献
15.
The spiral is one of nature’s more ubiquitous shapes: It can be seen in various media, from galactic geometry to cardiac tissue.
Mathematically, spiral waves arise as solutions to reaction–diffusion partial differential equations (RDS). In the literature,
various experimentally observed dynamical states and bifurcations of spiral waves have been explained using the underlying
Euclidean symmetry of the RDS—see for example (Barkley in Phys. Rev. Lett. 68:2090–2093, 1992; Phys. Rev. Lett. 76:164–167, 1994; Sandstede et al. in C. R. Acad. Sci. 324:153–158, 1997; J. Differ. Equ. 141:122–149, 1997; J. Nonlinear Sci. 9:439–478, 1999), or additionally using the concept of forced Euclidean symmetry-breaking for situations where an inhomogeneity or anisotropy
is present—see (LeBlanc in Nonlinearity 15:1179–1203, 2002; LeBlanc and Wulff in J. Nonlinear Sci. 10:569–601, 2000).
In this paper, we further investigate the role of medium inhomogeneities on spiral wave dynamics by considering the effects
of several localized sites of inhomogeneity. Using a model-independent approach based on n>1 simultaneous translational symmetry-breaking perturbations of the dynamics near rotating waves, we fully characterize the
local anchoring behavior of the spiral wave in the n-dimensional parameter space of relative “amplitudes” of the individual perturbations. For the case n=2, we supplement the local anchoring results with a classification of the generic one-parameter bifurcation diagrams of anchored
states which can be obtained by circling the origin of the two-dimensional amplitude parameter space. Numerical examples are
given to illustrate our various results. 相似文献
16.
We introduce a new notion called a quasi-Feistel cipher, which is a generalization of the Feistel cipher, and contains the
Lai–Massey cipher as an instance. We show that most of the works on the Feistel cipher can be naturally extended to the quasi-Feistel
cipher. From this, we give a new proof for Vaudenay’s theorems on the security of the Lai–Massey cipher, and also we introduce
for Lai–Massey a new construction of pseudorandom permutation, analoguous to the construction of Naor–Reingold using pairwise
independent permutations. Also, we prove the birthday security of (2b−1)- and (3b−2)-round unbalanced quasi-Feistel ciphers with b branches against CPA and CPCA attacks, respectively. 相似文献
17.
An orientation reversing involution of a topological compact genus surface induces an antiholomorphic involution of the Teichmüller space of genus g Riemann surfaces. Two such involutions and are conjugate in the mapping class group if and only if the corresponding orientation reversing involutions and of are conjugate in the automorphism group of . This is equivalent to saying that the quotient surfaces and are homeomorphic. Hence the Teichmüller space has distinct antiholomorphic involutions, which are also called real structures of ([7]). This result is a simple fact that follows from Royden's theorem ([4]) stating that the the mapping class group is
the full group of holomorphic automorphisms of the Teichmüller space (). Let and be two real structures that are not conjugate in the mapping class group. In this paper we construct a real analytic diffeomorphism
such that
This mapping d is a product of full and half Dehn–twists around certain simple closed curves on the surface . This has applications to the moduli spaces of real algebraic curves. A compact Riemann surface admitting an antiholomorphic involution is a real algebraic curve of the topological type . All fixed–points of the real structure of the Teichmüller space , are real curves of the above topological type and every real curve of that topological type is represented by an element
of the fixed–point set of . The fixed–point set is the Teichmüller space of real algebraic curves of the corresponding topological type. Given two different real structures
and , let d the the real analytic mapping satisfying (1). It follows that d maps onto and is an explicit real analytic diffeomorphism between these Teichmüller spaces.
Received 8 December 1997; accepted 12 August 1998 相似文献
18.
A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is
shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric
of neutral signature iff the pc conformal curvature vanishes. In the three dimensional case the corresponding result is achieved
through employing a certain symmetric (0,2) tensor. The well known result of Cartan–Chern–Moser giving necessary and sufficient
condition a CR-structure to be CR equivalent to a hyperquadric in
\mathbbCn+1{\mathbb{C}^{n+1}} is presented in-line with the paracontact case. An explicit formula for the regular part of a solution to the sub-ultrahyperbolic
Yamabe equation on the hyperbolic Heisenberg group is shown. 相似文献
19.
In this article, we prove that various classical conformal diffeomorphism groups, which are known to be essential (Banyaga,
J Geom 68(1–2):10–15, 2000), are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of
a cohomological equation. Furthermore, we study the orbit of a tensor field under the action of the conformal diffeomorphism
group for these classical conformal structures. On every closed contact manifold, we find conformal contact forms that are
not diffeomorphic. 相似文献
20.
In this article, we determine the spectral expansion, meromorphic continuation, and location of poles with identifiable singularities
for the scalar-valued hyperbolic Eisenstein series. Similar to the form-valued hyperbolic Eisenstein series studied in Kudla
and Millson (Invent Math 54:193–211, 1979), the scalar-valued hyperbolic Eisenstein series is defined for each primitive,
hyperbolic conjugacy class within the uniformizing group associated to any finite volume hyperbolic Riemann surface. Going
beyond the results in Kudla and Millson (Invent Math 54:193–211, 1979) and Risager (Int Math Res Not 41:2125–2146, 2004),
we establish a precise spectral expansion for the hyperbolic Eisenstein series for any finite volume hyperbolic Riemann surface
by first proving that the hyperbolic Eisenstein series is in L
2. Our other results, such as meromorphic continuation and determination of singularities, are derived from the spectral expansion. 相似文献