# A topological degree theory for rotating solutions of planar systems

@inproceedings{Gidoni2021ATD, title={A topological degree theory for rotating solutions of planar systems}, author={Paolo Gidoni}, year={2021} }

We present a generalized notion of degree for rotating solutions of planar systems. We prove a formula for the relation of such degree with the classical use of Brouwer’s degree and obtain a twist theorem for the existence of periodic solutions, which is complementary to the Poincaré–Birkhoff Theorem. Some applications to asymptotically linear and superlinear differential equations are discussed.

## One Citation

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## References

SHOWING 1-10 OF 35 REFERENCES

### Maslov index, Poincaré-Birkhoff Theorem and Periodic Solutions of Asymptotically Linear Planar Hamiltonian Systems

- Mathematics
- 2002

Abstract We study the relationship between the twist condition in the Poincare–Birkhoff fixed point theorem and the assumptions on the Maslov index for asymptotically linear planar Hamiltonian…

### A new fixed point theorem and periodic solutions of nonconservative weakly coupled systems

- Mathematics
- 2020

### Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

- Mathematics
- 1984

An index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse-type existence statement for periodic…

### Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth

- Mathematics
- 2017

Abstract We prove the existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of N planar uncoupled systems which, e.g., model some type of asymmetric…

### Degree Theory in Analysis and Applications

- Mathematics
- 1995

1. Degree theory for continuous functions 2. Degree theory in finite dimensional spaces 3. Some applications of the degree theory to Topology 4. Measure theory and Sobolev spaces 5. Properties of the…

### Existence of a periodic solution for superlinear second order ODEs

- Mathematics
- 2021

We prove a necessary and sufficient condition for the existence of a T periodic solution for the time-periodic second order differential equation ẍ + f(t, x) + p(t, x, ẋ) = 0, where f grows…

### A Topological Approach to Bend-Twist Maps with Applications

- Mathematics
- 2011

In this paper we reconsider, in a purely topological framework, the concept of bend-twist map previously studied in the analytic setting by Tongren Ding in (2007). We obtain some results about the…