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  1. Proceedings of the Steklov Institute of Mathematics
  2. Proceedings of the Steklov Institute of Mathematics : Volume 256
  3. Proceedings of the Steklov Institute of Mathematics : Volume 256, Issue 1, April 2007
  4. Minimal sets of Cartan foliations
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Proceedings of the Steklov Institute of Mathematics : Volume 296
Proceedings of the Steklov Institute of Mathematics : Volume 295
Proceedings of the Steklov Institute of Mathematics : Volume 294
Proceedings of the Steklov Institute of Mathematics : Volume 293
Proceedings of the Steklov Institute of Mathematics : Volume 292
Proceedings of the Steklov Institute of Mathematics : Volume 291
Proceedings of the Steklov Institute of Mathematics : Volume 290
Proceedings of the Steklov Institute of Mathematics : Volume 289
Proceedings of the Steklov Institute of Mathematics : Volume 288
Proceedings of the Steklov Institute of Mathematics : Volume 287
Proceedings of the Steklov Institute of Mathematics : Volume 286
Proceedings of the Steklov Institute of Mathematics : Volume 285
Proceedings of the Steklov Institute of Mathematics : Volume 284
Proceedings of the Steklov Institute of Mathematics : Volume 283
Proceedings of the Steklov Institute of Mathematics : Volume 282
Proceedings of the Steklov Institute of Mathematics : Volume 281
Proceedings of the Steklov Institute of Mathematics : Volume 280
Proceedings of the Steklov Institute of Mathematics : Volume 279
Proceedings of the Steklov Institute of Mathematics : Volume 278
Proceedings of the Steklov Institute of Mathematics : Volume 277
Proceedings of the Steklov Institute of Mathematics : Volume 276
Proceedings of the Steklov Institute of Mathematics : Volume 275
Proceedings of the Steklov Institute of Mathematics : Volume 274
Proceedings of the Steklov Institute of Mathematics : Volume 273
Proceedings of the Steklov Institute of Mathematics : Volume 272
Proceedings of the Steklov Institute of Mathematics : Volume 271
Proceedings of the Steklov Institute of Mathematics : Volume 270
Proceedings of the Steklov Institute of Mathematics : Volume 269
Proceedings of the Steklov Institute of Mathematics : Volume 268
Proceedings of the Steklov Institute of Mathematics : Volume 267
Proceedings of the Steklov Institute of Mathematics : Volume 266
Proceedings of the Steklov Institute of Mathematics : Volume 265
Proceedings of the Steklov Institute of Mathematics : Volume 264
Proceedings of the Steklov Institute of Mathematics : Volume 263
Proceedings of the Steklov Institute of Mathematics : Volume 262
Proceedings of the Steklov Institute of Mathematics : Volume 261
Proceedings of the Steklov Institute of Mathematics : Volume 260
Proceedings of the Steklov Institute of Mathematics : Volume 259
Proceedings of the Steklov Institute of Mathematics : Volume 258
Proceedings of the Steklov Institute of Mathematics : Volume 257
Proceedings of the Steklov Institute of Mathematics : Volume 256
Proceedings of the Steklov Institute of Mathematics : Volume 256, Issue 1, April 2007
Necessary conditions for an extremum in a mathematical programming problem
The curvature and hyperbolicity of Hamiltonian systems
Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices
Entropy estimations for motion planning problems in robotics
Structural stability of simplest dynamical inequalities
Approximation theorem for a nonlinear control system with sliding modes
Minimal sets of Cartan foliations
Hyperbolicity of periodic solutions of functional differential equations with several delays
General theories unifying ergodic averages and martingales
Dynamical systems with multivalued integrals on a torus
Attractors of the sine-Gordon equation in the field of a quasiperiodic external force
A method of graph transformation type for numerical simulation of invariant manifolds
Nondegenerate saddle points and the absence of mixing in flows on surfaces
Monodromy of Fuchsian systems on complex linear spaces
An additive cohomological equation and typical behavior of Birkhoff sums over a translation of the multidimensional torus
A dynamical approach to accelerating numerical integration with equidistributed points
C $^{0}$ transversality and shadowing properties
Proceedings of the Steklov Institute of Mathematics : Volume 255
Proceedings of the Steklov Institute of Mathematics : Volume 254
Proceedings of the Steklov Institute of Mathematics : Volume 253
Proceedings of the Steklov Institute of Mathematics : Volume 252

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Minimal sets of Cartan foliations

Content Provider Springer Nature Link
Author Zhukova, N. I.
Copyright Year 2007
Abstract A foliation that admits a Cartan geometry as its transversal structure is called a Cartan foliation. We prove that on a manifold M with a complete Cartan foliation ℱ, there exists one more foliation (M, $$\mathcal{O}$$ ), which is generally singular and is called an aureole foliation; moreover, the foliations ℱ and $$\mathcal{O}$$ have common minimal sets. By using an aureole foliation, we prove that for complete Cartan foliations of the type ℊ/ℎ with a compactly embedded Lie subalgebra ℊ in ℎ, the closure of each leaf forms a minimal set such that the restriction of the foliation onto this set is a transversally locally homogeneous Riemannian foliation. We describe the structure of complete transversally similar foliations (M, ℱ). We prove that for such foliations, there exists a unique minimal set ℱ, and ℱ is contained in the closure of any leaf. If the foliation (M, ℱ) is proper, then ℳ is a unique closed leaf of this foliation.
Starting Page 105
Ending Page 135
Page Count 31
File Format PDF
ISSN 00815438
Journal Proceedings of the Steklov Institute of Mathematics
Volume Number 256
Issue Number 1
e-ISSN 15318605
Language English
Publisher Nauka/Interperiodica
Publisher Date 2007-01-01
Publisher Place Moscow
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Mathematics
Content Type Text
Resource Type Article
Subject Mathematics
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