Let $M$ be a differentiable manifold and $f: [0,\infty)\times M \to M$ be a $C^1$ map satisfying the condition $f(0,p) = p$ for all $p\in M$. Among other results, we prove that when the degree (also called Hopf index or Euler characteristic) of the tangent vector field $w\colon M\to TM$, given by $w(p) = {\partialf \over \partial\lambda} (0,p)$, is well defined and nonzero, then we obtain global bifurcation. This extends known results regarding the existence of harmonic solutions of periodic ordinary differential equations on manifolds.
Global Bifurcation of Fixed Points and the Poincaré Translation Operator on Manifolds / M. Furi; M. Pera. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 173:(1997), pp. 313-331.
Global Bifurcation of Fixed Points and the Poincaré Translation Operator on Manifolds
FURI, MASSIMO;PERA, MARIA PATRIZIA
1997
Abstract
Let $M$ be a differentiable manifold and $f: [0,\infty)\times M \to M$ be a $C^1$ map satisfying the condition $f(0,p) = p$ for all $p\in M$. Among other results, we prove that when the degree (also called Hopf index or Euler characteristic) of the tangent vector field $w\colon M\to TM$, given by $w(p) = {\partialf \over \partial\lambda} (0,p)$, is well defined and nonzero, then we obtain global bifurcation. This extends known results regarding the existence of harmonic solutions of periodic ordinary differential equations on manifolds.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.