Trudinger N S, Wang X. The Bernstein problem for affine maximal hypersurfaces[J]. Inventiones Mathematicae, 2000, 140(2): 399-422.
2
Hasanis T, Vlachos T. Ricci curvature and minimal submanifolds[J]. Pacific Journal of Mathematics, 2001, 197(1): 13-24.
3
Gorodski C. Minimal hyperspheres in rank two compact symmetric spaces[J]. Boletim Da Sociedade Brasileira De Matematica, 1996, 27(1): 1-22.
4
Tomter P. MINIMAL HYPERSPHERES IN TWO-POINT HOMOGENEOUS SPACES.[J]. Pacific Journal of Mathematics, 1996, 173(1): 263-282.
5
Gorodski C. Minimal sphere bundles in Euclidean spheres[J]. Geometriae Dedicata, 1994, 53(1): 75-102.
6
Tomter P. On Dynamical Systems and the Minimal Surface Equation[C]., 1993: 259-269.
7
Brito F G, Chacon P M, Naveira A M, et al. On the volume of unit vector fields on spaces of constant sectional curvature[J]. Commentarii Mathematici Helvetici, 2004, 79(2): 300-316.
Smale S. Differentiable dynamical systems[J]. Bulletin of the American Mathematical Society, 1967, 73(6): 747-817.
2
Moon F C, Holmes P. A magnetoelastic strange attractor[J]. Journal of Sound and Vibration, 1979, 65(2): 275-296.
3
Rossler O E. CONTINUOUS CHAOS—FOUR PROTOTYPE EQUATIONS[J]. Annals of the New York Academy of Sciences, 1979, 316(1): 376-392.
4
Morris W Hirsch. The dynamical systems approach to differential equations. 1984.
5
Roberts J A, Quispel G R. Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems[J]. Physics Reports, 1992: 63-177.
6
Luo A C. Singularity and dynamics on discontinuous vector fields[C]., 2006.
7
Siegelmann H T, Fishman S. Analog computation with dynamical systems[J]. Physica D: Nonlinear Phenomena, 1998, 120(1): 214-235.
8
Howard J E, Humpherys J. Nonmonotonic twist maps[J]. Physica D: Nonlinear Phenomena, 1995, 80(3): 256-276.
9
Luo A C. The mapping dynamics of periodic motions for a three- piecewise linear system under a periodic excitation[J]. Journal of Sound and Vibration, 2005, 283(3): 723-748.
10
Mackay R S, Meiss J D. Linear stability of periodic orbits in lagrangian systems[J]. Physics Letters A, 1983, 98(3): 92-94.
Frederick P. GreenleafNew York University, New York, N.Y., USAMartin MoskowitzGraduate Center: City University of New York, New York, N.Y., USALinda Preiss RothschildColumbia University, New York, N.Y., USA
Lau A T, Paterson A L. Inner amenable locally compact groups[J]. Transactions of the American Mathematical Society, 1991, 325(1): 155-169.
2
Chou C. Minimally weakly almost periodic groups[J]. Journal of Functional Analysis, 1980, 36(1): 1-17.
3
Greenleaf F P, Emerson W R. Group structure and the pointwise ergodic theorem for connected amenable groups[J]. Advances in Mathematics, 1974, 14(2): 153-172.
4
Rothman S. The von Neumann kernel and minimally almost periodic groups[J]. Transactions of the American Mathematical Society, 1980, 259(2): 401-421.
5
Moskowitz M. On the density theorems of Borel and Furstenberg[J]. Arkiv för Matematik, 1978: 11-27.
6
Greenleaf F P, Moskowitz M, Preissrothschild L, et al. Automorphisms, orbits, and homogeneous spaces of non-connected lie groups[J]. Mathematische Annalen, 1974, 212(2): 145-155.
7
Kenig C E, Tomas P A. behavior of certain second order partial differential operators[J]. Transactions of the American Mathematical Society, 1980, 262(2): 521-531.
8
Carlos E Kenig · Peter A Tomas. On conjectures of Riviére and Strichartz. 1979.
9
Losert V. On the center of group C * -algebras[J]. Crelle\u0027s Journal, 2003, 2003(554): 105-138.
10
Moskowitz M. On a certain representation of a compact group[J]. Journal of Pure and Applied Algebra, 1985: 159-165.
We prove the Poincaré inequality for vector fields on the balls of the control distance by integrating along subunit paths. Our method requires that the balls are representable by means of suitable “controllable almost exponential maps”.