Morse index and bifurcation of p-geodesics on semi Riemannian manifolds
Monica Musso; Jacobo Pejsachowicz; Alessandro Portaluri
ESAIM: Control, Optimisation and Calculus of Variations (2007)
- Volume: 13, Issue: 3, page 598-621
- ISSN: 1292-8119
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topMusso, Monica, Pejsachowicz, Jacobo, and Portaluri, Alessandro. "Morse index and bifurcation of p-geodesics on semi Riemannian manifolds." ESAIM: Control, Optimisation and Calculus of Variations 13.3 (2007): 598-621. <http://eudml.org/doc/250003>.
@article{Musso2007,
abstract = {
Given a one-parameter family $\\{g_\lambda\colon \lambda\in [a,b]\\}$ of semi Riemannian metrics on an
n-dimensional manifold M, a family of time-dependent potentials $\\{ V_\lambda\colon \lambda\in [a,b]\\}$ and a family $\\{\sigma_\lambda\colon \lambda\in [a,b]\\} $ of trajectories connecting two points of the mechanical system defined by $(g_\lambda, V_\lambda)$, we show that there are trajectories bifurcating from the trivial branch $\sigma_\lambda$ if the generalized Morse indices $\mu(\sigma_a)$ and $\mu
(\sigma_b)$ are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly conjugate points along a trajectory using an explicit computation of the Morse index in
the case of locally symmetric spaces and a comparison principle of Morse Schöenberg type.
},
author = {Musso, Monica, Pejsachowicz, Jacobo, Portaluri, Alessandro},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Generalized Morse index; semi-Riemannian manifolds; perturbed geodesic; bifurcation; generalized Morse index},
language = {eng},
month = {7},
number = {3},
pages = {598-621},
publisher = {EDP Sciences},
title = {Morse index and bifurcation of p-geodesics on semi Riemannian manifolds},
url = {http://eudml.org/doc/250003},
volume = {13},
year = {2007},
}
TY - JOUR
AU - Musso, Monica
AU - Pejsachowicz, Jacobo
AU - Portaluri, Alessandro
TI - Morse index and bifurcation of p-geodesics on semi Riemannian manifolds
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/7//
PB - EDP Sciences
VL - 13
IS - 3
SP - 598
EP - 621
AB -
Given a one-parameter family $\{g_\lambda\colon \lambda\in [a,b]\}$ of semi Riemannian metrics on an
n-dimensional manifold M, a family of time-dependent potentials $\{ V_\lambda\colon \lambda\in [a,b]\}$ and a family $\{\sigma_\lambda\colon \lambda\in [a,b]\} $ of trajectories connecting two points of the mechanical system defined by $(g_\lambda, V_\lambda)$, we show that there are trajectories bifurcating from the trivial branch $\sigma_\lambda$ if the generalized Morse indices $\mu(\sigma_a)$ and $\mu
(\sigma_b)$ are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly conjugate points along a trajectory using an explicit computation of the Morse index in
the case of locally symmetric spaces and a comparison principle of Morse Schöenberg type.
LA - eng
KW - Generalized Morse index; semi-Riemannian manifolds; perturbed geodesic; bifurcation; generalized Morse index
UR - http://eudml.org/doc/250003
ER -
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