Second order Lagrangian Twist systems: simple closed characteristics

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Second Order Lagrangian Twist Systems: Simple Closed Characteristics

We consider a special class of Lagrangians that play a fundamental role in the theory of second order Lagrangian systems: Twist systems. This subclass of Lagrangian systems is deened via a convenient monotonicity property that such systems share. This monotonicity property (Twist property) allows a nite dimensional reduction of the variational principle for nding closed characteristics in xed e...

متن کامل

Fourth Order Conservative Twist Systems: Simple Closed Characteristics

On the energy manifolds of fourth order conservative systems closed characteristics can be found inmany cases via analogues of Twist-maps. The ‘Twist property’ implies the existence of a generating function which leads to second order recurrence relations. We study these recurrence relations to find simple closed characteristics andwe give conditionswhen fourth order systems satisfy the ‘Twist ...

متن کامل

Closed Characteristics of Fourth-order Twist Systems via Braids

For a large class of second order Lagrangian dynamics, one may reformulate the problem of finding periodic solutions as a problem in solving second-order recurrence relations satisfying a twist condition. We project periodic solutions of such discretized Lagrangian systems onto the space of closed braids and apply topological techniques. Under this reformulation, one obtains a gradient flow on ...

متن کامل

Closed Characteristics on Singular Energy Levels of Second-order Lagrangian Systems

We provide a lower bound on the number of closed characteristics on singular energy levels of second-order Lagrangian systems in the presence of saddle-focus equilibria. The hypotheses on the Lagrangian are mild, and the bound is given in terms of the number of saddle-foci and a potential function determined by the Lagrangian. The method of proof is variational, combining techniques to minimize...

متن کامل

Closed Characteristics of Second-order Lagrangians

We study the existence of closed characteristics on three-dimensional energy manifolds of second-order Lagrangian systems. These manifolds are always noncompact, connected, and not necessarily of contact type. Using the specific geometry of these manifolds, we prove that the number of closed characteristics on a prescribed energy manifold is bounded below by its second Betti number, which is ea...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 2001

ISSN: 0002-9947,1088-6850

DOI: 10.1090/s0002-9947-01-02882-3