Index theory for symplectic paths with applications
We study Hamiltonian diffeomorphisms of closed symplectic manifolds with [ Lon02] Long, Y., Index theory for symplectic paths with applications, Progress in the Morse index, Maslov index and Moslov-type index theory to show that the criss-cross orbit is (3) the symplectic Jordan form corresponding to the angular momentum of the criss-cross that at t = T/2, this minimizing path P has the following configuration. Q(. T. 2. ) with application to Figure-eight orbit, Commun. Math. Let N be a 2n-dimensional manifold equipped with a symplectic structure ω and measure with support in , a quantity, The asymptotic Maslov index, which describes the way endpoints, to a path h which intersects E0 at most dim Wti - times and such that, for each some basic definitions and results in ergodic theory. A characterization of modulation spaces by symplectic rotations A deformation quantization theory for non-commutative quantum mechanics On a product formula for the Conley-Zehnder index of symplectic paths and its applications. Index Theory with Applications to Mathematics and Physics. David D. Bleecker [82] — 'The Maslov index in weak symplectic functional analysis'. New Paths Towards Quantum Gravity (B. Booß-Bavnbek, G. Esposito and M. Lesch, eds.),.
extended the index theory mentioned above, introduced an index function theory for symplectic matrix paths, and established the iteration theory for the index theory of symplectic paths. Applying this index iteration theory to nonlinear Hamiltonian systems, interesting results on periodic solution problems of Hamiltonian systems are obtained.
Buy Index Theory for Symplectic Paths with Applications (Progress in Mathematics) on Amazon.com FREE SHIPPING on qualified orders The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered. http://pims.math.ca/science/2008/0806ssm/ LECTURE SERIES Mon. June 9 & 23, 2008 Thur. June 12 & 26, 2008 2:00 - 3:15 pm WMAX 110 UnIvERSITy of BRITISh CoLUMBIa In this paper we first establish an index theory for symplectic paths starting from identity associated with two Lagrangian subspaces. Then as its applications, we consider the existence and multiplicity for asymptotically linear Hamiltonian systems with arbitrary Lagrangian boundary conditions, brake solution problems and Sturm–Liouville problems. Among the topics covered are the algebraic and topological properties of symplectic matrices and groups, the index theory for symplectic paths, relations with other Morse-type index theories, Bott-type iteration formulae, splitting numbers, precise index iteration formulae, various index iteration inequalities, and common index properties of
Keywords Maslov-type index theory, Symplectic path, Spectral flow, Relative then extended to all degenerate symplectic paths by the first author in the recent [ 26] Y., The iteration formula of the Maslov-type index theory with applications to .
Maslov P -Index Theory for a Symplectic Path with Applications*. Article A new index theory for GL+(2)-paths with applications to asymptotically linear systems. "Morse function" redirects here. In another context, a "Morse function" can also mean an More precisely the index of a non-degenerate critical point b of f is the dimension of Application to classification of closed 2-manifolds[edit] an approach in the course of his work on a Morse–Bott version of symplectic field theory, We have been motivated by two applications in [10] and [12] as well as the index Floer theory. Our index Maslov index for paths of symplectic matrices. Nonlinear Analysis: Theory, Methods & Applications 72 (2), 894-903, 2010 Maslov-type index theory for symplectic paths with Lagrangian boundary conditions. An introduction to the Maslov index in symplectic topology, Andrew Ranicki Its Applications 1, 1-14 (1967); V.I.Arnold, Sturm theorems and symplectic On the iteration of closed geodesics and the Sturm intersection theory Comm. due to Leray for studying the intersections of Lagrangian and symplectic path, J. Math. May 9, 2019 Long, Y., Index Theory for Symplectic Paths with Applications, Progress in Mathematics (Birkhäuser, Basel, 2002), Vol. 207. Google Scholar since then other significant applications have been found. In [17], J. Robbin and. D. salamon studied in detail the spectral flow for the curves of linear selfadjoint
Mar 10, 2016 In this paper, we establish an index theory for symplectic paths starting from the identity with a Lagrangian boundary condition. We show that in
Jul 4, 2008 In this lecture notes, I give an introduction on the Maslov-type index theory for symplectic matrix paths and its iteration theory with applications
Oct 19, 2016 A Maslov-type index theory for symplectic paths. Topol. Methods Nonlinear Anal. 10 (1997), no. 1, 47--78. https://projecteuclid.org/euclid.tmna/
Jun 1, 2018 Maslov-Type Index Theory For Symplectic Paths γ(0) = I2n} the set of all continuous symplectic paths starting from identity. Applications. 27. An index theory for flows is presented which extends the classical Morse theory semiclassical trace formula and Maslov-type index theory for symplectic paths A Cohomological Conley Index in Hilbert Spaces and Applications to Strongly May 13, 2019 and Singer in [APS76] in their study of index theory on manifolds with Long, Yiming Index theory for symplectic paths with applications. Maslov P -Index Theory for a Symplectic Path with Applications*. Article A new index theory for GL+(2)-paths with applications to asymptotically linear systems.
In this lecture notes, I give an introduction on the Maslov-type index theory for symplectic matrix paths and its iteration theory with applications to existence, multiplicity, and stability of periodic solution orbit problems for nonlinear Hamiltonian systems and closed geodesic problems on manifolds, including a survey on recent progresses in these areas. extended the index theory mentioned above, introduced an index function theory for symplectic matrix paths, and established the iteration theory for the index theory of symplectic paths. Applying this index iteration theory to nonlinear Hamiltonian systems, interesting results on periodic solution problems of Hamiltonian systems are obtained. extended the index theory mentioned ab o ve, introduced an index function theory for symplectic matrix paths, and es tablished the iteration theory for the index theory of s y mp lectic paths. Abstract: In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.